I would fix the FF bugs ASAP. You'll have to do it eventually so put that at the top of your to-do list. The fixes probably aren't that hard. Thanks to firebug you could probably pin-point the bugs really fast.

It's probably better to put off the launch for a few days to avoid making a really bad impression to potential users.

My app is close to ready to be launched, but it only works in IE. Is it ok to launch with it working in IE only? Do you think I should let users know that it only works in IE?

One thing to remember is if it works in Firefox, it works on every platform. Windows people can still use your site even if they need to click another icon first...

IE-only means you lose all the Mac people, all the Linux people, and probably turn off the majority of the more clued-in Windows people.

Early adopters -- your target audience I assume -- don't tend to use IE.