What's the best way to do this?
Alternatively, are there places one could take a book to get it fixed? I really like my Thor omnibus and would be willing to spend a few bucks to fix it up (although I think Marvel should pay for it
With either a book press or flat weights--but yeah, if you've never messed around with repairing a book before you could easily do more harm than good. I practiced on junky books to begin with.
Do you live in the Northeast, like Mass. or something? I don't know why I think that. But if you do there should still be plenty of old school book repair people left somewhere not too far, check the yellow pages. I'm sure there are many places you could send a book to, but personally I'd prefer not unless I had a good relationship with them already or got some good recommendations. If you take it somewhere, just leave the dust-jacket at home someplace safe, no need to risk it getting damaged in transit.
Marvel's earliest attempts at omnibuses were much worse, it's one reason few are left on the market in good shape for some of the titles. Just hope the upcoming changes in single-issue production to save money by Marvel don't extend to collected editions like omnibuses and a return to those days. (I doubt it, but there's still room for improvement. While getting Marvel to pay for repair or replacement may be a far stretch, making noise publicly, like this thread, or contacting them directly to let them know you are dissatisfied, is not a bad idea. Also, you might contact the middleman retailer you ordered it from...unless it was eBay.)