I'll start: Veronica's "what's up" glitch, where she does not respond to any of the location triggers for her quest, "I Could Make You Care".
My personal workaround (this may not work for everyone) was to visit all of the easy triggers (visit this place and talk to someone/just walk around), do the White Wash, then go complete Vault 11. She will trigger during the movie in the Vault (she talked about the Van Graff's energy weapons for me). Then walk into McCarran's terminal building (I personally used the doors closest to Colonel Tsu), walk around a bit, then walk back out the same doors. Walk a long arc through the camp while headed towards the door to outside, and she will trigger again (I believe this trigger was about the Followers of the Apocalypse). And finally (though I revisited several locations trying to find which event would trigger it last), head to the Boomer Museum and listen to the boy's whole speech about the Boomers (do NOT interrupt), and Veronica should trigger a final time, thus beginning the "I Could Make You Care" quest.
I hope this workaround helps some, as it may just be a personal solution (though I hope not).
Now, I also have a request for help.
I am currently attempting to do the Free Quest: "Old School Ghoul" with Raul, but I have become stuck on Ranger Andy, who will not trigger a response from Raul. After investigating, I believe it is a scripting error (where you must not have made the comment that gets you his special technique, or even talked to him at all, which is highly unrealistic considering how early the game introduces him, how easy the speech check is, and how long it is before you're powerful enough to get up Black Mountain). If it IS a scripting error, there is, sadly, nothing I can do about it except wait for a patch to be released, and hope that they found the time to fix it (which is a crap shoot, at least to me). However, if anyone has found a workaround for this problem (short of starting the game all over, as I just hit level 30 and there is no way I could bring myself to do that at this point), I would be delighted to hear it.
Feel free to answer my question, or post questions/requests for help of your own. This thread is for all companion-related problems/solutions.
P.S. Dear Bethesda moderators, If one of you happens to read this post, I do hope you remember to fix small things like this. Not that my whining helps the likelihood of it, but scripting errors are something we console players cannot fix, no matter how we try. I especially (and politely) request that you fix the scripting error in "Old School Ghoul" that I have mentioned, because I am aware of a small mod that the PC community was able to make in about 15 minutes that fixes the problem completely; it is very frustrating knowing that a solution is only just out of my reach, save for my decision to buy a console version of your game. Thank you for your time.