Unfortunately for the time being there is no quicker way to check the actual degree of quality (ex. 6/10, 7/10, etc.) other than to hover over the keyword analysis tool (magnifying glass) next to each keyword in Adwords. The editor is supposed to be updated "soon" with more QS data so we can see how keywords are doing at a glance, so keep your fingers crossed that they launch it shortly.
I actually made a suggestion to our Google reps to display the QS score underneath the grade (Great, Poor, Ok) right in Adwords so that we can optimize keywords even faster, but they indicated that such a change would most likely be rolled into an editor update. Here's what I suggested: [forums.searchenginewatch.com...]
I'm assuming that you already opted to display the quality score column so that you can at least see which keywords are "Great", "Ok" and "Poor" in Adwords. If not, at the adgroup level, under the keywords tab, click on the customize columns link and make sure that "Show Quality Score" is selected. Now at least you'll be able to see the quality score right in Adwords, but you'll still have to hover over the keyword analysis tool (magnifying glass) to see the actual degree of quality for each level (Great, Ok and Poor).
Make sure to put in a request to Google for more transparency with the quality score to be able to optimize campaigns faster. The more people requesting the same features, the faster they tend to roll them out.