Several. It’s nice when he acts accordingly. Such as spamming his eye shock laser on rakks and stuff. But there are just a lot of issues with him.
-He’ll use his eye shock laser on a lot of bosses instead of meleeing them. Such as Terra and large based bosses like Bunker (which is understandable since it flies) and the big Boom turret. He becomes useless on those kinds of fights. Deathtrap doing nothing but spamming his crappy shock laser on things like Bunker and Handsome Dragon is just blegh. Happens on Handsome Sorcerer too, iirc. Pretty big waste in Hyperius too.
-The slowness of Robot Rampage. It makes the skill basically pretty bad against enemies that move a lot. Which are mainly gun enemies, of which there are legion. Gets a lot better in Tiny Tina’s DLC with all the melee enemies, though.
-The Stare. The weird description on it saying that it has an AoE like effect, but it’s just a powerful version of his eye laser, but fire element. The fact that he uses it on armored enemies makes basically no sense whatsoever.
Yeah, I’m aware. If you die, though, it’s a real pain. Because if you build up 80-100 stacks (or more) and you are used to that damage, you get to deal with it all over again. Rational Anarchist helps by putting them at 25 if you should die to offset that, which is 43% gun damage right off the bat. The issue being that Anarchy is Gaige’s only dps skill outside of SLF and The Better Half. The former which can hurt your dps on some guns, the latter only working 50% of the time, and also dependent on the gun.
Additionally, Typecast Iconoclast is great. When it procs. It’s a 30% chance. Which can happen somewhat often between killing enemies (especially places with lots of small ones, like Sanctuary Hole with varkids or Frostburn Canyon with the humans and spiderant mix, assuming you don’t die) and reloading your gun. And you can’t put it at 60% with the Legendary Anarchist COM because you have to be lv62 to even begin farming for it.
Issue being that Gaige can’t really raid, which kinda sucks because she’s the only other female character and I really like female characters. 
Well, she can. But she’s built upon not dying. Which is really hard when you don’t really know the mechanics of the raids themselves and haven’t even beaten most of them. I’ve beaten Terra twice and still only recently learned how his pattern works and how prone it is to weird glitches. Only beat Pyro Pete once, and that was by cheesing him through the upper level glitch in the corner + shock Sandhawk + Bee (before it got nerfed).
My other issues with Gaige are scaling issues. I remember it all being pointed out how many issues her LBT tree has. Though maybe that was strictly OP levels and not just UVHM by itself? Please correct me if that’s the case. The issues I remember were…
-More Pep’s modifiers are way too low. 20% slag and 10% for other effects is incredibly low for five points, especially considering they’re calculated by taking a % of your current number. 20% of a 20% chance to slag (SMG) is 20% -> 24%. That’s awful. It gets worse with the other elements. 15% to set an enemy on fire (SMG). That’s 15% -> 16.5%.
-Strength of Five Gorillas also seems really low. 15% extra melee damage for Gaige is abysmal, though iirc it’s more for Deathtrap since his melee damage by default is insane and stacks like crazy with Upshot Robot. Though I imagine the 15% gets better when you have With Claws.
-Electrical Storm on the inaccuracy focused character makes no sense. Expecting Gaige, who will always have at least -40% accuracy (20 Anarchy stacks) if not worse is a really big deal. It procs for DT as well, but he’s not super reliable in terms of focusing enemies you need to die in a specific spot for Electrical Storm to really shine.
-Shock and AGH. I read this is a mechanical issue (which may have been fixed? not sure). Which is that when SoA procs on an enemy, it overrides Gaige’s ability to apply shock DoTs on the enemy, severely hampering her entire tree. Which is made worse by the fact that SoA doesn’t do nearly as much damage as Gaige could deal through electrocution damage, even with just blues and purples. Which is to say nothing of Electrical Storm proccing it. It also prevents Electrical Burn from proccing (which is a huge deal). It makes Evil Enchantress worthless (unless you switch to fire/corrosive) because you can’t override it and thus are amping pathetic damage. Also makes Wires Don’t Talk worthless as well. Along with One Two Boom should it proc a DoT.
Some other issues not related to LBT.
-Made of Sterner Stuff. I seem to recall this being a waste of points because 5% damage reduction is nonexistant and 15% melee damage is why it’s really picked up for DT.
-Death From Above being weird because it procs if you get slightly hit into the air. Such as by a varkid. Which causes you to tear through your Anarchy stacks. Not having control over it (such as it only working if you manually jumped) makes it really hard to properly use.