I don't have a problem with the term "transgender." I think it's nice to have an umbrella term, particularly if you're in the process of figuring out your gender identity, as I have been and more-or-less still am.
I do, however, have an issue with using the term as a verb. A trans woman I'm acquainted with said it best, though this is only paraphrasing: Calling someone transgendered implies that at some point someone or something transgendered them. You don't call gay people gayed.
It also bothers me when people say "a transgender." It seems.. belittling? I don't know what it is, exactly. It's like when people talk about "the gays."
I'm also not sure why, but the term "transsexual" just bothers me on some deep, vague level. Deeply ingrained negative associations, perhaps. I honestly couldn't tell you.