*** WARNING: INCOMING RANT *** (also, comic sans)
I'd say there are three things about Rifts that really annoy me. The first two are completely superficial and are related to formatting, errors and tone. The last one is mechanics.
Going into specifics:
(spoilered because as I said, these 2 are really pet peeves of mine and don't reflect the actual quality of the rules. Those are terrible, but that's not spoilered)
#1: the proofreading is terrible, author doesn't know the difference between distance, area and volume, instead measuring everything in "feet" for example (this is a minor nitpick, I guess). Multiple exclamation marks, "the sure sign of an insane mind" as Discworld would put it. Layout, order of chapters, some rules are just randomly mentioned in a completely unrelated part of the book - I can't exactly remember but I think the actual rules for punching or dodging or something are found only in the Giant Mecha section, even if you want to apply it to man vs. man combat, and some other global rule that should be somewhere central, can only be found in the class section for the Psycho, I think. Insanity, I think it was, even tho it could be caused by seeing a scary monster instead of just a side effect of being a Psycho.
#2: the tone of several sections is extreeemely condescending of other RPG game designers. The "15 levels" thing I mentioned, rambles on about how "other games" don't know how many levels are too hot or too cold, but 15 is "just right". Then there's the part of the Alignments was just shitting on other games tables while presenting the "correct" table of Alignments such as "is selfish" or "likes shellfish" or something like that.
EDIT: Also, why is everything just a dumb acronym? Like, you need to memorize what every ability score means and it's just 2 or 3 letters, often the same letters for different stats, like "Physical Prowess", "Physical something else". Neither is your strength, I think. And the stat that has "mental" in it isn't your intellect, it's your charisma or something. The stats that says "strength" are either your beauty, or your Psi points. P.P.E. is your magic energy (which is called "psychic energy", even though psychics don't use it). O.C.C., S.D.C, R.P.A., C.S... oi! Last time I encountered that it was a game designed by Derek Smart.
#3: here we get to the meat of the issue. Rules are a mess. They make no sense... character generation takes forever, to fill the skill lists for example. Classes aren't just unbalanced, they are not even fit for the same game. Like, one class comes from a 80's saturday morning cartoon and has the power of friendship and reading books, and the other is MurderKillRoboto that can one-shot buildings with nuclear missiles and is a dragon who also reads minds. And a Jedi. But has a 5% penalty to the Accounting skill so that balances out.
I thought I had more to say about the rules, but it has been a while since I actually read them. I do remember hating them a lot, and not even compared to other games that "did it better"... they just make me angry for some reason.
Arguably the best part of the game are the sourcebooks, like you can get the Japan book and make a cool full conversion cyborg with a dragon body, or there's some fun backstory about Brazilian leopard men and stuff. The "Rifts in Space" sourcebooks for Phase World are also really cool, but they apparently don't even take place in the same dimension as Rifts Earth or something because Rifts Earth outer space doesn't exist or something (or at least you can't get from one to the other except by some magic portal), so essentially it's its own game and characters shouldn't just transfer over. The core book mentions that "because of rifts, races from other Palladium books can also be in Earth" which is barely touched on. But this adventure booklet told me that character X was an Elf and I had no idea how to stat him (because I didn't own PFantasy), it was just completely out of place, because no effort is made at all to actually make you feel like there are dwarves or elves palling around with MegaDamage guns. It's almost a sidenote.
EDIT 2: Hm, there's this post at story-games that describes a lot of the stuff that's being mentioned here, so probably it's a good idea to just check this out and save some time:
http://www.story-games.com/forums/discussion/9965/sell-me-on-wait-for-it-the-palladium-system-i-kid-you-not