Mutation in pre-mRNA sequence
Yes, you can find mutations in the genomic DNA which affect splice acceptor sites. Wikipedia lists the following outcome:


Mutation of a splice site resulting in loss of function of that site.
Results in exposure of a premature stop codon, loss of an exon, or
inclusion of an intron. 
Mutation of a splice site reducing specificity. May result in
variation in the splice location, causing insertion or deletion of
amino acids, or most likely, a disruption of the reading frame.
Displacement of a splice site, leading to inclusion or exclusion of
more RNA than expected, resulting in longer or shorter exons.


The article lists two interesting papers: 

Lim KH, Ferraris L, Filloux ME, Raphael BJ, Fairbrother WG (2011). "Using positional distribution to identify splicing elements and predict pre-mRNA processing defects in human genes". Proc. Natl. Acad. Sci. U.S.A. 108 (27) 11093–11098.

Ward AJ, Cooper TA (2010). "The pathobiology of splicing". J. Pathol. 220 (2) 152–163.

Both papers are open access.