If you are using physical shearing methods (as I suppose if you ask about end repair protocols), your DNA fragments should not have blunt ends after fragmentation.
Besides being less stable, blunt end fragments are required for correct and efficient ligation of library adapters, so not performing this step will result in heavily reduced amount of correctly ligated fragments or even complete fail of library preparation.
Thanks Edoardo. Yes I use physical shearing. I have two exome sequencing data with lots of mutations with low variant allele fraction. The density plot for variant allele fraction in one of these samples looks like bellow. I am trying to figure out what happened for this sample. Our reagents was spoiled for some reasons. Can this be a reason for getting such a strange distribution of mutations?
I was actually the guy who invented random shearing followed by repair of the ends for DNA shotgun sequence analysis a long time ago (Anal Biochem. 1983 Feb 15;129(1):216-23). If the repair doesn't go well, then your primary problem would be that your libraries would be less complex than desired and you would sequence the same molecule as PCR duplicates. This sounds like the opposite problem to what you are seeing. First, I would suggest testing your sequences for PCR duplicates to eliminate them. The very low frequency mutations seem likely to represent PCR and/or sequencing error rather than authentic mutations. It is critical in next gen sequencing to come up with experimental criteria to differentiate mutations from PCR/sequencing errors.