A large number of WordPress 2.7 users have had to make do with using the much slower browser uploader  because they have had no “select files” button.

If you’re one of these people (and I was), then breathe easy because it’s not a Flash problem and it’s not WordPress 2.7 (at least, not directly).

For some reason, those that used the automatic upgrade option missed out on a single file, called “swfupload.swf”, and therein lies the problem.

The solution, thanks to fryewiles in the WordPress.org forum, is to simply upload the missing file to the appropriate folder on your server:

/wp-includes/js/swfupload/

You can find a copy of the file by downloading the latest copy of WordPress, unzipping it on your hard drive and going to the folder above.

Then upload the file, either using your hosting cPanel or by FTP with software like Core FTP.

A very sincere thank you to fryewiles for solving this problem for us all.