Hi Mark;
Good question. I'll defer to Carl or Steven on this one for the best answer ...but a quick answer (from me) is that GR is still relevant and is underpinned by Newtonian mechanics. I did a couple of threads on spirals recently:
http://www.iceinspace.com.au/forum/s...ad.php?t=64705
and;
http://www.iceinspace.com.au/forum/s...ad.php?t=64837
I try to summarise the long conversations at the end so I hope there's a quick answer at the ends of the threads for you.
Also, just because masses drift away from each other in a galaxy, doesn't mean that gravity field strength 'disappears'. It remains and diminishes with distance squared. The influence of other masses drifting into the spiral arms then adds another influence.
Gotta go.
Cheers
PS: The answer to your question is also "its a scale thing". GR is used over larger distances eg: intergalactic distances. Not so much influence in intra-galaxy distances.