When is Seconds_Behind_Master too big? My mysql_slave got stuck on an error and built up to being 200,000+ Seconds_Behind_Master. Should I rebuild it and start from scratch, or let it catch up by itself?
IMHO

Let it catch up. 

The Seconds_Behind_Master reading is not what I rely on to see if catching up is possible or worth it. Don't be afraid at the number reported.

You have to look at the server's setting for expire_logs_days. If your slave is so far behind that the binary log file has been deleted, then you need to re-image.