I assume you've tried WHERE score > 2?
Also, try re-evaluating it - ie:
WHERE count(search_table.word) > 2
The other question is, do you actually need the score or not? The query might work if you leave the score out of the field list, but just include it in the where clause.
Also, do you need to GROUP BY on the search_table? Quite often that can screw up aggregate functions like COUNT().
Also, if the machine is under your control, try upgrading to the latest version of MySQL which I think is 3.23.49 at the moment...
cheers,
Matt