My well pump is fed by a 40a 240v circuit. I noticed that sometimes when the power cycles, or I manually cycle the breaker, that the circuit is only getting 120v. If I flip the breaker a few more times this resolves itself. Do I need a new breaker, or is this likely something else?
Almost certainly a bad breaker. Square D Homeline is the cheaper model than the QO breakers, but you'll have to replace it with another Homeline breaker since the QO breakers won't fit in a homeline panel.
BTW, I noticed that you are running 10ga wire. That isn't rated for 40 amps. And to be running 40 amps to a pump, it must be a heck of a big pump. What's it being used for? Commercial irrigation?
Also, it may be a loose connection someplace, like the wires themselves or the feed to the panel.
Also check the wire connections on the breaker.
That is THHN wire which has the size written right on it. It's 10 AWG which needs a little thinking about:
240.4 Protection of Conductors. Conductors, other than flexible cords, flexible cables, and fixture wires, shall be protected against overcurrent in accordance with their ampacities specified in 310.15, unless otherwise permitted or required in 240.4(A) through (G).
(D) Small Conductors. Unless specifically permitted in 240.4(E) or (G), the overcurrent protection shall not exceed that required by (D)(l) through (D)(7) after any correction factors for ambient temperature and number of conductors have been applied.
(G) Overcurrent Protection for Specific Conductor Applications. Overcurrent protection for the specific conductors shall be permitted to be provided as referenced in Table 240.4(0).
Motor and motor-control circuit conductors: 430, Parts II-VII
And in 430.32 they allow overcurrent device to be 140% of motor rating. And in Table 430.52 they allow 250% of Full Load Rating. Not actually seeing the motor nameplate, most likely the 40A breaker is legit.