I'll give some examples; I don't think spot can mean "dot" though.
- I can't get this spot off my pants! (a small area) | point doesn't work
- This is the spot. We're here guys! (a physical location) | point sounds weird
- This massage is great; that hits the spot. (a location on the body) | point doesn't work
- Will you spot me? (a verb for weight-lifters) | point means s/t else
- Don't touch that spot; it's dirty! (a small area) | point means s/t specific; for example, the tip of a sword
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- At this point, I knew I won. (a point in time) | spot means physical location
- a point in time (a moment) | spot doesn't work
- You're missing the point (the message/purpose) | spot means s/t else
- A triangle has 3 points (dot) | spot doesn't work
- Point me in the right direction (verb) | see "spot me" above
Hope this helps!