Greetings from another century house owner!!

First thing I want to mention...if you have Murphys....give it away, seriously. It's nasty & it takes absolutely months for the smell to go away!

For those tiny paint splatters....you can use a fine grit (package will say 0000 or 1000) sandpaper or steel wool. You likely have a shellac finish on the woodwork and it is very good at protecting the wood & making splatters like you have come off easily.

For the bigger splotches, although tedius, see if you can chip at the edges with a single edged razor blade....carefully. Keep the sandpaper handy for the small bits left over.

Just so you know...mine has the little spots of paint like yours too. It drove me crazy at first and I have cleaned up some....but after 7 years, I have moved on to other, more important projects.

You will realize after time that the things that bugged you initially are not as important later on.

Best piece of advice I got after getting my place....wait a full year before doing anything that cannot be un-done.

For some excellent "Old House Specific" advice....go here!
https://www.wavyglass.org/

Nothing you present will be new to them. They have seen & done it all.

I was given Dow Great Stuff Work Wipes at a home show recently. They are for cleanup, of course, but I was shocked when I tried them on dried latex paint on woodwork and they cleaned it off! You might give them a try. Even if they don't work, they're awesome to have around the house when you are doing projects!

@lilion....I'll have to try those too! Thanks for the tip!

They clean up so much stuff, uncured construction and tile adhesive, paint, and of course, Great Stuff! They sell them at Lowe's I know.

Nail polish remover works really well for removing latex paint, but you'd want to test it and make sure it wouldn't damage with the underlying finish.

Al is right. The solvent for shellac is alcohol and ammonia, so keep those away. Sometimes goof off applied sparingly will dissolve the paint but not the underlying finish. Painters often use a rag soaked in mineral spirits then wrapped around a putty knife.

Stain markers work great to cover scratches, though amber shellac and a fine brush may be all you need as your finish looks pretty light.

if you use the mineral spirits, use caution...it is flamable!!