Some simple commands to use to search for adaptor-dimers:
In Illumina data:
This works for a standard Illumina genomic DNA library made with TruSeq V3 Y adaptors, and since the Y adaptors are RC's on each end, works equally well for read 1 and read 2.
For small-rna library/single stranded RNA library, The previous command will work for read 1. For read 2, use something like: