Pool Pump is not reliable

[KarlW65]

The switch looks clean -- I watched it while powering on.

In both cases it spins a few turns. If it works, the spinning accelerates otherwise it just stops. Either way the switch "engaged" (2 copper prongs push connection onto shaft)

[Poconos]

Sure sounds like the starter circuit switch. Even though it looks like it's closing, could be pitted contacts. Being an intermittant problem points to that too. Use some 400 or 600 grit wet-or-dry sandpaper (auto stores) or a small flat file (preferred) to dress the contacts. Usually they are silver and soft so you don't need to be agressive. See if that solves the problem.
Al

[tenax]

if you hadn't replaced the capacitor, i'd wonder about that as well..is there a way to wire it wrong..i.e. backwards or something.

[Poconos]

Starting capacitors are non-polarized so it doesn't matter which way they get wired. Usually when a capacitor fails it shorts or opens and doesn't become intermittent.
Al

[Ohm_Boy]

It would be worthwhile to connect a meter to the power wires at the motor, and watch it while it tries to start. That way, you can see if there is any significant voltage drop under load. If there is, the wiring to that point is suspect.

Always be careful with the wires exposed when the power is applied.

[anotherpyr]

Starting capacitors are non-polarized so it doesn't matter which way they get wired. Usually when a capacitor fails it shorts or opens and doesn't become intermittent.
Al

Good thing too considering you're dealing with an alternating current and that electrolytic capacitors can explode if the polarity is wrong.