When you try to add new filter rules or edit/delete existing ones and get the following error:

There was a problem parsing your filter rules: parse error: evaluating Sieve script

Here is what you need to do to get rid of this problem.

I think that after a zimbra update the existing filter rules are somehow incompatible and are causing this troubles.
This Bugreport describes some similar problem.

To get rid of the old filter rules i try to delete them using the zimbra admin console.
Some more Information on the commands can be found in the Zimbra Wiki.

List existing filter rules:

zmmailbox -m <account-email-address> -z getFilterRules
# z/--zadmin   use zimbra admin name/password from localconfig for admin/password

Delete a filter rule:

zmmailbox -m <account-email-address> -z deleteFilterRule "name displayed in getFilterRules"

After deleting all filter rules i could add new ones using the zimbra collaboration suite.