I've had my surname wrongly spelt a few times (strangely, my BAEC no. was OK and the system didn't seem to notice the wrong name).
It's been no problem at check-in etc., however I did once have difficulty entering at immigration (I think it was Taiwan) when they asked me to show them my return booking. Although it was only 1 letter out, the Taiwanese official wasn't happy. Once his boss came out and I showed him the BC I'd just arrived on and my confirmed onward booking in the same (wrong) name, it was OK. Took a while, though (and for once, the Filipinos waiting behind me had to wait in the queue for ages).

Depending on what Passport you hold and what visa requirements you have, this may be your only problem IMHO.

As others have said, if the TA made the mistake I don't see why you should have to pay for the change.