N1-methyladenosine (m1A) was proposed to be a highly prevalent modification in mRNA 5'UTRs based on mapping studies using an m1A-binding antibody. We developed a bioinformatic approach to discover m1A and other modifications in mRNA throughout the transcriptome by analyzing preexisting ultra-deep RNA-Seq data for modification-induced misincorporations. Using this approach, we detected appreciable levels of m1A only in one mRNA: the mitochondrial MT-ND5 transcript. As an alternative approach, we also developed an antibody-based m1A-mapping approach to detect m1A at single-nucleotide resolution, and confirmed that the commonly used m1A antibody maps sites to the transcription-start site in mRNA 5'UTRs. However, further analysis revealed that these were false-positives caused by binding of the antibody to the m7G-cap. A different m1A antibody that lacks cap-binding cross-reactivity does not show enriched binding in 5'UTRs. These results demonstrate that high-stoichiometry m1A sites are exceedingly rare in mRNAs and that previous mappings of m1A to 5'UTRs were the result of antibody cross-reactivity to the 5' cap.