Its not that they mess up the extension API. The extensions just are not configured to work with 3.5.
When you build a FireFox extension, you specify the minimum and maximum version of FireFox that its built to work with. The majority of extensions that dont run in FF 3.5 just have not had their maximum version increased to 3.5.
If you want to manually attempt to make the extensions work, you must download their xpi file. Rename it to a .zip. Extract install.rdf and open it up in notepad. Search for these lines.
<em:minVersion>3.0b5</em:minVersion>
<em:maxVersion>3.0.*</em:maxVersion>
Change the maxVersion line to 3.5.*
Put the new install.rdf back into the zip file, rename it back to a .xpi file and install. Presto.