1). light dot spots in center of actor eyes
You could rotoscope this out, but it’s likely a waste of time because rotoscoping is a time-consuming process. Light reflections in an actor’s eyes are generally considered a good thing; DoPs will add eye lights for this purpose.
2) hot spot where direct light was hitting arm.
You might be able to color this in with the 3-way color corrector found in the PRO version of Final Cut.
FCE doesn’t have it. However, you might be able to hack the filter into FCE. Get a project from FCPro, with the 3-way CC applied on a clip. You may be able to copy it onto your clips somehow (sorry I haven’t tried this).
If you manage to get the 3-way CC onto your clip:
Use the secondary controls (limit color) to pickup the hot spot on the flesh tone. It will require some fiddling of the controls. I’m just glossing over the process here, it’s a little hard for me to explain.
I would read the manual (or figure out what all the buttons and knobs do even though you probably dont have the FCP manual).
With the hot spot isolated, color it in by dragging the right color wheel on top towards orange/flesh tone color. Lower white level or gamma just a touch, to bring the brightness of the hot spot down.
2- If you could post up a .jpg of your problems, it might help a lot. I can’t be sure if I understood your problem correctly and am addressing them properly.
3- In retrospect, it probably would’ve been easier to fix these problems at the shoot. Diffusion/soft light, flags, and wiping the actor’s skin dry (and possibly adding foundation) are tools which might have helped you solve your problem.