Can only one chipped and broken teeth on a saw blade make the actual cut very uneven

If you are talking about a circular saw blade, in a skilsaw or a table saw, then yes. Especially if it is kind of a thin kerf blade.

Blades vibrate and deflect like crazy while you’re cutting. Better blades will have a heavier, stiffer plate to reduce the wobble and produce a smoother cut.

But with any blade it is very common for the teeth to get more worn on one edge than the other, and this will cause a fairly large force that will make the blade deflect off the line and track poorly in the cut. If the blade is brand new, and you just hit a nail and damaged a couple teeth, it is also likely the blade was slightly deformed from the shock.

A blade is already experiencing lots of uneven forces trying to steer it through a cut all kinds of ways you don’t want it to go just due to the wood grain. Add in uneven wear, imbalances and warps that produce wobble, and other non-uniformities, and you can end up with some seriously raggedy cuts.

An expensive, heavy, pro/shop grade blade can be repaired, sharpened and balanced. For job site grade blades, we just toss them when they start misbehaving. If it turns your workpiece into a smoking ruin, its time.

If you mean a hand saw, usually not, unless the tooth set was deformed.