1. Derpy was a BG pony and she got krap loads of love. Just appearing in one episode doesn't mean we shouldn't love her.
2. As others have pointed out, she's a showmare. It's kind of her job to boast her skills on-stage, and the lie about defeating the Ursa Major was a story to entertaint he crowd. I mean, come on, LOTS of good stroies are fictional. If she were to tell them the amazing feats of her trips to Pony-Mart, I doubt that'd draw as big a crowd.
Also, just wanna point out, RD, AJ, and Rarity give Trixie such a hard time for being a boaster and for lying.
RD - Biggest boaster in Ponyville. Just look at the Mare-do-Well episode. She was pretty much doing what Trixie did in that ep.
AJ - A bit more modest, but still likes to boast and show off her skills (like in the episode where she was competeing with RD).
Rarity - Sweet and Elite. Need I say more?
3. She was giving out a free show, and a bunch of random ponies in the crowd were heckling her. If I were Trixie, I'd be pretty mad too. However, she actually handled it pretty well. She kept her stage persona and challenged them to prove she wasn't the greatest. They accepted her challenge and she beat them fair and square (and the audiance seemed to like it).
What she did to Rarity was a bit over the top, but then when you consider that her show was being constantly interrupted by these hecklers, she was probably just taking out her anger on her, whilst also trying to effectivly silence any other neigh-sayers at the same time.
So all-in-all, Trixie was actually the victim of that episode, not the Mane 6. I support Trixie 'cause she's an interesting character. She's skilled with magic, and she has a lot of potential to be a good recurring cast member. She's adorable, she's confident, and I can imagine she'd actually get along well with Twilight if they met again.
I also feel sorry for her losing everything she had in that one night, and being left all alone, when she's done nothing to deserve such a fate. Hopefully she has friends elsewhere in Equestria that were willing to help her out.