Why would there be a spike in coverage within a gene in RNA seq data?
Without knowing how your libraries have been prepared and sequenced it is hard to tell if that is due to a technical or biological source.

However, there are a few bias sources in RNA-seq (which aren't an issue in DNA-seq)

One of them is that if you used a "random-hexamer" protocol, they're known to not be so random after all. See: Hansen KD, Brenner SE, Dudoit S. Biases in Illumina transcriptome sequencing caused by random hexamer priming. Nucleic Acids Res. 2010;38: e131. 

You might also have a contamination from other species that would present a sequence identity for that part more specifically.