Can methylation from DNA get copied to RNA during transcription?
I don't believe anything should change in the majority of DNA->RNA transcription. DNA methylation typically occurs on the non-watson crick side of Cytosine so it shouldn't affect the base-pairing.

However, there are a few hypothetical situations that would result in alterations of the transcribed RNA. The sponatneous deamination of the 4' amine would convert the base into uracil. If there is an additional 5' methyl, the 5-methyluracil would be recognized as Thymine.

(edit) I've talked with several genomics folks about this topic and it turns out that M5Cytosine is very resistant to deamination due to the presence of the Methyl group. As a result, the instance that I have just described is actually very rare.



5mCytosine to Thymine deamination

The other situation would be to errors in DNA proofreading. Does the 5mCytosine affect the fidelity of RNA polymerase? I honestly don't know but it would be worth examining.