-- I would bet money that a lot of the hate for her comes from her "dissing" the Chief, as the Chief is the player's avatar. A lot of people hate Del Rio's guts too, primarily because he slags on the Chief (IMO).
Dissing the Chief is fine. If it were handled well. Like i said, subtlety would have worked better here. Palmer is a bad character, and a lot of that comes from her being used as a hammer, for narrative purposes.
And considering how major character she is, why don't we get to know her any better really? What's her problem with scientists? That they created her? (This would make an interesting twist actually, that she actually hates being a Spartan, despite volunteering, like it wouldn't be what she imagined to be or something like that).
Palmer sharing the same, annoying to some, "dudebro" aspects, and in a way those are upped with her: no helmet, dual-wielding (not outside of Spartan's abilities really but neither it is a standard for them), solo mission, general attitude hurt her too. Is it too much to ask for a professional Spartan like we've used to see? There is a lot of leeway within limits of professionalism. OTOH, if 343i realizes it, they can use these later on for great effect, by deconstructing these, doubly so if they use Palmer for this. See what happens when "reality" ensues.
A problem with dudebro attitude Spartan IVs exhibit is that they're the only ones to do this in Halo 4, for no reason. Everything else is relatively professional, and that's the case for most Halos, some oddities aside.
SIVs (shivs?, that's my new nickname for Spartan IVs) having laid back attitude wouldn't be a problem in itself but it is exaggerated too much. Again, lack of subtlety. Or something. (And i've heard that special ops forces are in a way more laid back, but then they're highly capable people and motivated, their high-risk duties give them a bit more leeway when it comes to off-duty and general attitude, no?)
Del Rio works well in Halo 4, IMO, because we see someone in command who isn't actually suited for that (indeed, in-universe Del Rio seems to be excellent sort for logistics and other non-direct-command stuff, but complex situations that require snap decisions...). Of course, we are not explained this in-game, so all people see is horribly incompetent leader, not an officer who is out of his element, forced to his current command due to UNSC internal politics (which, by the way, could use more attention in the games too. Explain ONI and UNSC branches, stuff like that, so that people don't need EU to understand more. Also can be used for general depth in the story).
Lasky is badly handled, after more interesting Lasky we saw in the Forward Unto Dawn. There is a total disconnect between FUD and Halo 4 Lasky, IMO.