Methylation on gene-body and 3'UTRs if copied to mRNA can potentially regulate post-transcription modifications or expression regulation. But I'm not sure if they are maintained after transcription or if they get all de-novo methylation.
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.
There is an article in PNAS Conservation and divergence in eukaryotic DNA methylation who used:
next-generation sequencing to investigate the DNA methylation patterns in eight divergent species, including green algae, flowering plants, insects, and vertebrates. Their data allowed a comprehensive comparison of whole-genome methylation profiles across the plant and animal kingdoms, revealing both conserved and divergent features of DNA methylation in eukaryotes.
So there is some conservation.