Well... the underlying errors went away, but it seems the new SPDY patch broke being able to handle multiple hosts on the same SPDY connection now (it worked under 1.3.10 just fine).
For example, we have a SSL cert for both digitalpoint.com and dpstatic.com (dpstatic.com is a cookieless domain for serving static content), so SPDY attempts to use the same connection for multiple hosts. See SPDY session list here: http://f.cl.ly/items/0T1u3g0h0e1A0D1g2N0s/Image%202013.01.08%2011:59:48%20AM.png
With the SPDY patch for 1.3.11, now requests to *.dpstatic.com are *actually* being sent to digitalpoint.com (and getting a file not found). So somehow during a SPDY connection, the host for an individual request is being ignored somewhere along the way.
Top browser is Chrome (SPDY connection), bottom browser is Safari (no SPDY support)... the end result is a SPDY connection will yield different results vs the "traditional" SSL connection: http://f.cl.ly/items/3K1Q2N1I3B000c0b0614/Image%202013.01.14%205:52:31%20PM.png
Again, this worked as expected (ability for SPDY to properly share a connection across multiple hosts) with 1.3.10.