What is your mapper of choice for mate pairs generated by Illumina? I have heard about Novoalign, but haven't checked any newer options yet. (I know that some people just reverse complement the reads to PE orientation and then use their favorite mappers.)
Have you noticed any biotinylated adapters in your data?
The protocol that Illumina uses for creating of mate-pair libraries doesn't generate only long mate-pair reads with expected insert sizes, but also proportion of reads in PE orientation, which are in this case "contamination". Here is the nice picture with insert sizes that illustrates this - PE contamination is in red and MP reads are in green.
Here is the link to Illumina mate pair protocol
I will appreciate your comments and shared experiences.