In molecular biology, a "half register" is a misalignment between two identical sets of repeating units of nucleotides within two copies of the same chromosome (one set of repeating units per copy of the chromosome), where repeating unit "A" from one set is inappropriately aligned with repeating unit "B" on the other set. For instance, "ABABAB" on one set would be aligned with "BABABA" on the other set instead of the correct "ABABAB" with "ABABAB".
In living organisms, half registers create genetic mutations that can cause developmental abnormalities or cancers.
The information in this writeup was taken from the science dictionary at http://biotech.icmb.utexas.edu/; I oversaw the development of the dictionary (the website was mothballed in 1998) and I believe I wrote the entry this is based on.