We had an outage for our app shown on the dashboard below. There was no appengine outage notification and nothing on twitter so it looks like it was local to us. There was nothing noticeable in our logs (no increased failed requests, just silence). It lasted about 40 minutes and was noticed by our customers (we get about 1.5 requests per second). We are a paying customer but not premium (additional $500 per month) so can’t email google about the issue. What’s the best way to get more information / resolution of the problem?

Subscribe to the app engine mailing lists. There’s usually a flurry of activity on the general one when !@#$ hits the fan.
https://groups.google.com/forum/?fromgroups#!forum/google-appengine
There’s usually a message posted to on the downtime-notify list too, but it usually shows up after a bunch of people complain. On the other hand, there’s much less fluff to sort through.
https://groups.google.com/forum/?fromgroups#!forum/google-appengine-downtime-notify
In terms of resolution, you file a production issue (search for “production issue template” in that first mailing list), and wait.