Your father has probably looked up at the gutters from the driveway and decided they are fine. He may be right. The real question is whether they carry water away from the house before the first cold night, because water that stops in a gutter has nowhere to go except over the edge, behind the wall, or down against the foundation.
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Check these before you decide
If it is raining, or has just rained, go out and watch the gutters. Look for water spilling over the front edge or running down the siding behind them. Look for sections that dip toward the middle, and for joints where the gutter has pulled away from the fascia. Then look at the bottom of each downspout. Water should leave onto a splash block or extension that carries it several feet from the foundation, not pool at the base of the wall.
Count the work before you count the gutters. Note how high the lowest edge sits off the ground, how many corners and downspouts there are, and how steep the roof is. Then ask whether someone can stand at the bottom of the ladder. Most of the trouble in gutter work comes from reaching too far to one side, and a second person at the base is what keeps that from happening.
If you do it yourselves
Use a sturdy ladder that reaches the gutter without you standing on the top rungs, set on firm, level ground, with someone holding the base. Wear gloves, because the debris is wet and sharp. Work in short sections, bag the debris as you go, and then run a hose from the high end of the gutter. Watch whether the water moves toward the downspouts or sits in a low spot. A slow leak at a joint is much easier to fix in the autumn than in January.
If you hire it out
Ask for the scope in writing before anyone climbs. It should say whether they clean both sides of the house or only the front, whether they flush each downspout, whether they bag and haul the debris or leave it in the yard, and whether they check the splash blocks. Ask whether the crew brings its own ladder, and ask for the certificate of liability and workers' compensation coverage rather than a verbal yes. Photos of the gutters before and after are a good sign that someone is actually looking.
Compare two quotes by what each one includes, not by the total alone. One may cover the flush and the haul-away while the other covers only the scooping, and those are two different jobs. Also ask who comes back if water still runs over the edge after the first hard rain. Local Help for a Widowed Father in St. Louis is a reasonable place to start if you are looking for names.
What to do tonight
Take a flashlight outside and look at the downspouts. If one is plugged with leaves, see whether you can clear the top end from the ground. Then tell your father you noticed it, and let him say what he would like done about it. He will likely want to be part of the decision, and that is a good thing.