If you want to meet CE requirements for noise immunity and emissions, a two-layer board would help a lot.
Generally speaking, there is no problem with putting components on both sides of the board, in the same place. If you had a two (or more) layer board, you’d probably want to put a ground or power plane between them. However, you can’t do that with a single-layer board. So you should watch out for a fast digital chip interfering with an analog circuit. It would be inadvisable.
For example, put a microcontroller on one side and a high input impedance buffer on the other. But putting decoupling caps opposite the chip is probably a good plan.
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