Actually I’ve just discovered the root cause for this issue.
I’ve fully deactivated BPS and reverted to the default .htacess but the issue persisted so it was NOT caused by BPS.
I’ve deactivated mod_pagespeed from my server and now the Add Media button works.
So, the issue is caused by BOTH wordpress 3.5 for not being fully compatibile with mod_pagespeed beta and by mod_pagespeed beta itself for not being fully compatible with wordpress 3.5…
I hope a fix will follow soon in wordpress 3.5.1 because my server still uses the beta version of mod_pagespeed even though version 1.0 was finally released a few months ago and having pagespeed disabled is not good because the site loads really slow without it.