What can I do with a rectangular mirror with a frame I don't like?

You can have it reframe. Unframed you can put felt dots on back and use it as a table runner. Very showy, looks great with candles and centerpiece.

Patricia to change the frame of your mirror use almost anything.

You can decorated it. Place shells on it , glass flat beads like from flowers or vases. Paint it.

You could always replace the frame too.

My mom used mirrors on her dining room table a lot under her center pieces.

You could remove the frame and replace it with one that’s morebyiur style. Or just paint the current frame if it’s just the color you don’t like. I like the other suggestions of using the mirror on a table as a runner, that sounds very pretty.

Can you decorate the frame?

Either paint it, stick beads and buttons around it. You could decopatch with napkins and PVA. Or you could glitz it up with glitter by painting frame with PVA then glitter, then when dry PVA again to seal it. Or you can apply gold leaf. Hope you could use some of these ideas.