I've tried to create rule for highlighting rows that do not start with a date stamp (e.g "2013-07-05").
I've created a regex that works in RegexBuddy and seems to work in the Edit Highlight dialogue in the Highlight Testing textbox:
But when applied on the log, this does not work:

(?m)^(?!(\s*\d{4}-\d{2}-\d{2}.*$)).*$

Any idea why?

I applied it on the log using the highlight dropdown, and removed all other highlighting for that log.
But, then all rows, also the ones starting with a date, was highlighted.

I have, however, found a workaround:
By adding a highlighting for all as the last rule and then another rule just above it in the list, for rows starting with a date, resetting the hightlighting.
Then using these two rules together gives the wanted result.

Btw: I have a couple of feature suggestions:
1. An option on Highlighting rules to Invert Match (i.e. Not highlighting matches, but all rows not matched)
2. An description field for the rule (for comments, or to replace the actual rule in the dropdown - especially useful for regex rules)

Nice. Thanks!