How does one measure the length of telomeres?
Again, not an expert, but I found this article seems to say it pretty well: 

Telomere's are most commonly measured by qPCR of the repetitive regions with degenerate oligomer sequences such as "TTAGGG and CCCTAA repeats"  Although articles like this one appear to advance measurements in vertebrates, this reference from 2011 implies two techniques continue to be most common: 

1) qPCR with the appropriate oligos and then running them on an agarose gel

2) Southern blot of a restriction digest that leaves the telomeres intact  

Clearly sequencing techniques don't do well with repetitive sequences such as this, so in general this still seems like the most common method.  

This would indeed be quite destructive, at least for the cells used, though a biopsy would be enough, though apparently micrograms of DNA are required.  Kind of a large amount. 

The accuracy would then be limited to that of the gel or blot.  That would generally be a percentage of total length, I think 2% might be obtainable, but I'm not sure about that part.