Powering some chips through resistors is a common technique to keep out supply noise. In addition it avoid possible damage due to a latch-up event. Especially the older CMOS switches are a little prone to Latch-up, if for some reason current flows through the internal protection "diodes".
The 10 K values are rather high, but probably still OK. My normal values is more like 100 Ohms.
The CMOS switches use very little power and thus can easily be powered through resistors. Still they can produce quite some noise spikes when switching.
I just realized that if one would change the divider ratio, the right divider would be 32 and not 16. So the change would be just setting the CLR signal to ground. As a side effect the test frequency would be a little lower so it may need some small adjustments in the software too.
The CLR pulse is really odd - it normally should not be sufficient to reset the counter, but for some reason it does.
Another point to check may be the ground connections. Maybe there is a broken link somewhere. The layout seems to use a ground plane, but with quite some slits on the top. These slits can negate the function of a true ground plane. So it might be worth to check the ground with the scope at a few critical points.
A 70 MHz scope should be sufficient. The problem is more with where to have the ground.
Thanks for the explanation! It seems high, but the voltage after the resistor is still over 5V (for the positive rail).
About changing the ratio. How likely is it to help with the 74HC74 problem, considering that the output of the '393 is quite fine? I also doubt being able to get the source code and not only the .hex yo change the frequency.
The pulse in weird indeed, but hey. If it works, don't fix it!
The picture is the top layer of the board. I tried to keep the plane as continuous as possible, but it isn't that great around the 74HC74 to be honest. I'll try soldering a bodge wire from pin 7 directrly to the power supply ground to see if it helps.
Taking a look at the board I just noticed that the trace that carries the output signal of the 74HC74 runs under the +5V line. Can that be problematic somehow?
Update: I soldered the wire. No difference at all. I'm starting to think the problem is the chip itself