I power up my project by plugging a power supply into the power socket.
There's a microcontroller inside. Sometimes it boots successfully, sometimes not. I think it depends on how much I fumble while inserting the power connector. If there's an flaky connection right at the start, perhaps it causes a problem.
First question: is that a likely explanation?
Second question: how can I fix it? Is there some way to deny power until the connection is steady? Or is it better to reset the MCU as described here? (I don't understand how that solution would work though.)
There's a 470uF capacitor on the analog side of the circuit on the 9V side of the 5V regulator which supplies the MCU. Could that be part of the problem?
My main constraints are cost and board space. Power consumption isn't a huge concern: I measured consumption as 70mA, and typically at least 150mA would be available.
Edit
Here are (what I think) are the relevant parts of the circuit. Apologies for not including these earlier.
And here's the analog part of the circuit: