Most forums give the admin the right to delete posts (for whatever reason you choose). If they don't automatically give you the right to do so, many open source forums allow for plugins that'll do the job.
As far as the level of tedium, that greatly depends on how many posts you get, and what kind of posting method. There is generally a setting that will allow posts to either be submitted automatically or go through the admin for review. Either way, a simple program can be written to scan the content of the post looking for keywords (that you define). Once these key words have been found a flag can be raised to notify you of a post you don't find to be kosher.