How is the mRNA transported out of the endoplasmic reticulum? In eukaryotes the nuclear envelope is continuous with the ER, so what helps it out of that?

I'd make a comment if I could, but I don't think mRNA ever enters the ER. When a ribosome is building a protein destined for export or for being inserted into the membrane, it travels to the ER membrane and binds to a protein in that membrane called Sec61, which guides the new peptide sequence through the membrane. However the portion of the ribosome that reads the mRNA is always in the cytoplasm. So the mRNA never enters the ER, it just gets close the cytoplasmic side of the ER membrane.!Image of the protein translocation process

Have an image from a German website.