Disney Quest gets very busy on rainy days (suprise - suprise!) because it's all "undecover".
The quiet periods are during the peak times at the main parks - mid-morning to late afternoon.
Having said that - we went twice last year in the evenings and can report that there were quite short queues - or no queue at all for most of the attractions.
The Buzz Lightyear Astroblaster and the Pirates Adventure were the most popular but we only waited a maximum of 15 minutes for anything - this was in August 2004.
I would try to avoid the weekend days as - like the water parks - they tend to be busier with the local population.
It is a good fun place for the kids but if it is crowded I imagine it would be unbearable! (I don't do queues!)
There are some real fun "family" things to do - the raft ride and pirates were the best two for us - although watching the kids build a roller coaster and then watching them on the monitor as they rode it was hillarious (we bought the video!).