if sperm contains only 50% of someone's DNA how can it be used to identify someone?
The comment from @User137 pretty much gets it: the mix of all sperm cells in even a small sample will contain the whole genome on average. So in the hair example in the comments above, there are probably a good number of dead cells hanging onto the hair, enough for analysis. Meiosis will redistribute the DNA sequences inherited from mom and dad randomly, so each sperm is in theory a unique patchwork of that person's genome, but overall the genome will be covered well. Single-cell work, on the other hand, is technically very challenging.

[edit: here is an article describing methods for low-input analysis of forensic samples. Unfortunately paywalled.]

To directly answer the OP on uniqueness: absolutely a single sperm is that unique for each person, in principle. There are lots and lots of genetic variants in each human, and everyone represents a unique mix. It is estimated that 1/1000 places in the genome of each person differ from any other person, on average (for substitutions). there are 3*10^9 places in the genome for this to be the case, which gives you a very large number of differences, ASSUMING that you can actually ascertain all those differences. [edit: for a discussion of these stats see here.]

The technical problem with forensics is that often they only look at a few places in the genome (microsatellites usually), because it is relatively expensive and hard even with recent technology to look at more than that in any detail. This leads to the non-trivial possibility of misidentification with the standard battery of loci. This possibility never goes away entirely, but it becomes very small with more data. I am not a forensic scientist, possibly they have gotten more comprehensive or the methods have changed in recent times.

[edit: here is a document that has what appears to be a readable introduction to DNA forensics, including technical discussions of some drawbacks of marker panels used by for instance the FBI of the USA.]