Adobe Flash has to be installed manually as far as I know, but it is a simple process. Just download it from Adobe's site, extract the tarball and throw the libflashplayer.so file in /usr/lib/mozilla/plugins (for 32-bit Slackware) or /usr/lib64/mozilla/plugins (for 64-bit Slackware). There is a SlackBuild at slackbuilds.org and there is a SlackBuild included with Slackware64 in extra/, so there are plenty of ways to install flash system-wide.
ActiveX is 100% Windows-only so if any site demands an ActiveX control then you will be unable to use that site on any non-Windows platform. ActiveX controls are pretty large security risks and there are relatively few sites that use it (excluding Microsoft's own sites), so this is not generally a problem.
If you want to see all errors, try starting X with
Code:
$ startx 2>~/Xerrors.log
Or, if you want to see *all* output (not just errors),
Code:
$ startx &>~/Xoutput.log
Then when you exit X you can browse the file that should have been created to find any errors and decide whether or not they are serious.