Watch the Outlining D Half Dim online guitar lesson by Fareed Haque from Bebop Improv Survival Guide
The basic chord, arpeggio and scales on D 1/2 dim 7. There are more and more alternatives as you get into more dissonant chords. Check out the b9 (Eb) as well as the Nat 9(E natural). You will find that sometimes one note sounds great when ascending (going 'up' the scale) and another note sounds better when going down or descending. That's the beauty here.
In a rigid '7-note scale per chord' approach, your ear will hear things like this and your hands and brain wont let you go to them. You will find that different altered notes will sound good on a chord within the same measure or even same phrase! Don't be afraid! Just go for it!