Upload a zip archive and let WP unzip it and attach everything to a page/post (or not).
Try this: Open up the upload-media-by-zip.php file and locate
WP_Filesystem() (line 257). Surrounding it are three lines labeled 1, 2, and three. Uncomment those.
This problem happens only on some server setups, I haven't experienced it personally which makes it difficult for me to provide a better solution. If you have one, please share.
Sounds like you're using 2.8. Update.