We worked on this today with our web filter. The issue is that the app such as Dragon Dictation (and some others) is trying to send non SSL traffic over the SSL port 443. Some web filters do not like this since they think that someone is trying to circumvent the filter to bypass it. We had to unblock the following 2 ips over port 443 to make this work.
205.197.192.52
208.94.122.120
1st side note - We use St. Benard's iprism for our district web filter and our Education Service Unit use a Lightspeed filter. Eventhough their filter is not supposed to be doing anything with our traffic, we still had to allow port 443 to those ips on both filters.
2nd Side note - We had the same issue with SIRI and had to unblock 17.174.4.9 port 443 on both filters again to make SIRI work as well.
It seems that this may something to look for if you can't find something being blocked in your web filter.
Hope this helps someone.
Jason