I'm getting a similar issue - I've got SS2.4, dataobject_manager and swfupload installed.
When I upload a file using swfupload, the file uploads, but then the progress bar just says "Processing..." and nothing happens.
I've added SWFUploadConfig::debug(); to my /mysite/_config.php and I see the debug output but there's no error messages there. The last line in the debug output is "SWF DEBUG: Event: uploadProgress: File ID: SWFUpload_0_0. Bytes: 15350. Total: 15350"... which I think is just telling the progress bar to update.
I've developed several sites under Silverstripe and they all use dataobject_manager and swfuploader, but it seems like they're not compatible with SS2.4.
There's also another thread that talks about uploads being broken in SS2.4, and patching some of the files - I tried that but it didn't seem to make a difference. I don't know if it's related. The post is here: http://silverstripe.org/general-questions/show/281744?start=8#post284383
How do I get swfupload/dataobject_manager working in SS2.4?