I have used Dojo since .4 and have not had many cross browser issues, and the few I have had have mainly been concentrated in IE6 I think I had one issue with FF in that time and it was in one of the dojox libs and one issue with Safari which was a bug with Dojo and was resolved with the next release.
As for it being heavy, Dojo does have a wealth of libraries in it, but the Require.js build system strips the production release of Dojo down to what you need, as well now that they are using requires you can bundle all of your assets up into the build.
On the subject of ImageBundle I don't know the implementation details, but I would assume that it is just generating HTML Image Maps and/or CSS sprites which is pretty easy to do in PhotoShop as well there are a bunch of online generators where you upload a set of image files and it generates the coordinated for each one for you. Here is a link to a sprite generator http://csssprites.com/ . I don't think you will find a pure JavaScript library that does that for you, as most people just use PhotoShop or one of the online applications.