I would remove one of those 1000uF power supply filter caps, allowing you to move the entire regulator assembly back away from the big SMT chip. As it is, you have unregulated power too near the SMT pins. And, 2000uF of filter capacitance is more than plenty. I'd even consider removing two of those caps, if you can find a way to use the space.
16V might not be sufficient for those PSU caps. Amveco says the unloaded voltage for that transformer is 13V, and rectification will push that to over 18V. Now, in your design, the transformer is always loaded, so the question is whether the load will bring the transformer voltage down enough before the rectifier. I wouldn't change anything right now, but if the caps explode on startup or you measure the peaks with an oscilloscope and find them over 16V, swap some 25V caps in there. (You do have access to an oscilloscope, I hope...)
Since space is tight, I'd definitely use a monolithic bridge. Not only are they smaller, but the diode matching is likely to be better than a collection of random discretes, so there will be less switching noise.
Speaking of switching noise, I don't see any snubber caps on that bridge...
I don't like the circuitous trace from the N pad to the cap. Perhaps the easiest fix is to move the L pad so it uses the left pad of the fuse holder instead, and then put the N pad where the L one was and try to squeeze the trace between the fuse and the mounting pad. If there's not enough room for that, it looks like you can make some room. The filter section is rather loosely packed. Also, you could try switching to an 0.047uF cap in the line filter.
I'm not sure it makes any difference, but I would prefer to put the oscillator's load caps between the osc and the IC, simply for inductance reasons.
Finally, I like halman's idea of using the second winding separately instead. If you go with the 70001 transformer, fewer filtering caps, and the monolithic bridge, you may have enough room for two filter and regulator sections. You'll probably need to use an LDO on the 8V side. You should be using high-performance regulators anyway, due to the high speeds this circuit will be running at. Ye olde 3-terminal regulator is generally only good out to 10 kHz. Beyond that, you're depending 100% on the bypass caps. A good regulator can help out a lot.