The high stray capacitance will in fact help here (except for the crystal oscillator); the high inductance of the ground "loop" (we can't see how it is connected from the rightmost rail where the leads from the "regulated source" are connected to the leftmost rail from where the '51 gets GND, so that connection is at the far bottom apparently) will be a killer.

A basic internal-memory-only, LEDs-and-RS232, 5V '51 circuit with the commonly available 24MHz chips does not need necessarily a double(plus)-layered board to work flawlessly, but of course this is valid only if the tracks are kept reasonably short (especially for the oscillator/crystal tracks). I don't say it will pass EMC and similar tests, nor that it is a good design practice, and it is certainly not professional; but for basic homebrew hobby circuit it will work.

Of course, proper decoupling etc. is a must, the reset IC is highly recommended.

There is no need to scare people to death; but they should be aware of the basic risks and their remedy.

JW