In many of the aspects where it lacks rules, 5e also lacks guidelines, or they are incredibly broad, like 'this is possible, now design the rules for it, GO!'
this.
5e is an incomplete, half-assed product which was to be expected with Mearls.
... Could you give an actual example of this, please? The skill system lacking explicit examples isn't the end-all for declaring an entire system half-assed, and from doing all of the math possible in a system without 50bajillion splat books I can tell you that the math of the system is definitely well-thought out and balanced.
Quick example: undead, more specifically skeletons: the MM clearly tells you that you can make skeletons out of almost anything, but fails to give you any kind of indication how. All it provides you is 3 examples. If you want to make a skeleton out of any different kind of creature, you need to figure out a 'skeleton template' all by yourself.
Hell, the whole MM is just a collection of monster entries, with 0 support regarding how monster rules actually work (like for example 'how is Natural Armor calculated?') or how to actually change/improve existing monsters.
Undead in general? Okay. Let's flip to page 282 of the DMG. There we have the stats for an NPC or created skeleton and zombie.
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Skeleton is +2 dex, -4 int and cha. The creature gains vulnerability to bludgeoning damage, immunity to poison damage and exhaustion and can't be poisoned. Oh, and has darkvision to 60ft and can understand (but not speak) languages it knew in life.
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Zombie is +1 str, +2 con, -6 int, -4 wis, -4 cha. The creature gains undead fortitude, immunity to poison damage, can't be poisoned, darkvision to 60 feet and it can understand (but not speak) languages it knew in life.
As far as templates go... you wanted them, there they are. Other templates (such as vampire or lich) are either part of the creature's stat block, or just aren't made yet. Hoowever, they
do have dracolich, half dragon, skeleton, zombie and vampire. They also have the creation of Slaadi and Mychonids, but those aren't exactly "templates" as such. The actual rituals for
creating something other than what a PHB resource says you can
is entirely up to the DM, however. Sort of like it was in
every edition of D&D besides maybe 3.5, given players had some resources that they could draw on from the DMG and the DMG only (magic items, crafting and PrC's... and the 5e DMG has 2/3 of those as well, just not the expectation that all DM's will allow all of their players to draw on the DMG resources). The Monster Manual has always been the dominion of the DM.
As for monsters... well, let's tackle natural armor quick. It works just like light armor, where it sets the creature's AC to a certain amount and then adds in the critter's dex bonus. So it's not exactly rocket science to figure out. It's also stated on page 7 of the monster manual, under the heading "armor class." Next for changing and modifying monsters... Well, let's look in the DMG at pages 273-283. All of these pages are dedicated to the math behind creating and modifying monsters of certain CR's, and with tables for making NPC humanoids different based on race, or granting creatures certain abilities and how those abilities affect over-all CR.
As far as I can tell, the separation of monster advancement into the DMG had to do with spacing in the Monster Manual and reaffirming that the monster manual and DMG are supposed to be linked together as
DM tools that players can have access to if the DM is willing to make it so. It's not like a player is exactly going to be an ancient red dragon or lich, and it might not fit the theme of a campaign to have a few months of downtime for item creation, so it makes sense to limit some things to the realms of DM approval or non-player options.
As well, it's a new system. Certain things are not yet present as options that a DM could make as their own conversion, but which will likely be added in later (Like a Monster Manual 2, likely with more templates, for example). A lot of the things that you find "unfinished" or "missing" just haven't been converted yet due to the lack of real manpower on the D&D staff as of right now, or are being rolled into new adventure paths to let you get a look at how they work in an "official" adventure. The adventure paths also have at least one free online companion that comes with them, with Tyranny of dragons more dedicated to monsters (and thus DM tools), and the Princes of the Apocalypse companion focusing on player options with new races and spells. I would not be surprised if the Underdark path comes with more shadowy, demonic options (or maybe even psionics), and if future paths continue the same trend.
Anyway, to answer the question of the thread: The major differences between 3.5 and 5e would be balance... but to a much greater degree, the difference is in player entitlement. Since I haven't exactly seen anyone going into this one, I'll explain what I mean for a second.
In 5e, as in 1e, 2e, and to a lesser degree 4e, there is a separation between what players have access to and what a DM has access to. While all players can X (core classes and spells, core races, etc), they do not necessarily have access to Y (knowledge on how to build "balanced" encounters or custom monsters, random loot table generation, special monster abilities, etc). The separation is supposed to just reaffirm the roles, both to make a DM's job easier and ti give the world a bit more of a fantastical edge to it, where not everyone can do everything, or where certain capabilities are just not possible for certain beings to comprehend (like an invisible stalker being perma-invisible, as someone already brought up in the thread). It can be abused by a DM, and was abused horribly by Gygax back in the day, but for the most part it's just there to make the story or combat aspects flow more smoothly. Things like a god of war granting their champion access to abilities or spells that PC's cannot normally achieve (and that are unbalanced in PC hands), or the creation of unique magical items that tie strongly into the game's plot, but that can't be replicated, are good examples of this separation.
3.X broke from this system by making every single creature, item, spell or plot-important device function along the same design. Every skill possible was codified and given circumstantial modifiers, every monster progressed like it had levels of monster X, and over all things were as complex as they could get. Players could police DM's and had massive control over the story's flow and direction in a way they never had before (or since). A DM could still make new or unique things if they wanted, but then that opened them up to being learned and used by players or rule-0 DM fiat land, and 3.X is the system where such a thing began to carry such negative connotations. Since everything ran along the same system, players had justification to feel entitled to quite a lot of the more broken things that were meant to be variants or DM tools, and as stated before by sooooooooooo many people, this could culminate in unforeseen ways to make quite a few unbalanced and "overpowered" options. Anything the DM could do, PC's could break better*.
This also led to far more work on the DM's end, as the rules for PC creation were often complex and incredibly involved, and all creatures and challenges basically functioned like PC's. Creature type led to different stat blocks, had different hit dice, ability score and size progressions, granted feats at different rates, had differing immunities and defenses, and forced a lot of work and memorization for what would likely only last 1-3 rounds of combat with a party. Keeping certain plot-device abilities out of the hands of a PC became a chore, and setting DC's for mundane challenges consisted of consulting mile-long pages of charts and tables, accounting for every variable and possibility. While it was "fair" and "consistent," such a system sacrificed convenience in the most ritualistic way possible, and forced a DM to spend a lot of time on mechanics that could have gone to story.
Personally, after having DM'd both, I have to say that 5e is far more easy to work with from a DM perspective, and less of a headache numbers wise for both me and my players. I don't have to worry about how many feats and ability score increases my monsters have, I can just make or find something challenging for my players in 15-20 minutes by fiddling with its HP, AC, proficiency bonus and ability modifiers as fits the monster, and maybe give it a unique ability or two if I spend another 5 minutes thinking about it. I don't have to worry about gaming the system to give the monster the best PrC's, items for their expected treasure horde wealth (likely magic items on their person to increase the challenge), or my players just steam rolling 4 hours of work on my BBEG because I forgot about one of their horrendously broken combos while designing the boss.
I'm alright playing 3.5, but don't think I'll go back to DMing it. It takes too much time building PC's as is in the system, I don't want to have
that much out of game work as a DM ever again. I also don't want to have my players hijack the story the instant they hit level 6 or complain about enemies having tools that they lack, as that has taken up literal hours of game session in the past, and I am honestly just sick of it. The division between PC and NPC is something I wholeheartedly support. >_>
*Read to the tune of "Anything you can do, I can do better"