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I also think that current technology also has problems sequencing the bp near the start of a sequence.

Sort of. Current DNA sequencing technology breaks the DNA up into short pieces, sequences the pieces, and then uses software to reassemble them by looking for places where the fragmentary sequences overlap. It's basically the mother of all DIFFs. Telomeric DNA (the DNA at the ends of chromosomes) consists of many repetitions of the same short (<10) sequence of base pairs, so there is no pattern for the reassembly process to latch on to. So it's not the ends per se that are problematic, it's any long sequence that is devoid of structure. Chimps, for example, have telomeric DNA in the middle of one of their chromosomes. This is an example of "smoking gun" evidence for macroevolution. See http://www.gate.net/~rwms/hum_ape_chrom.html

I wonder if nanopore sequencing will ever be good enough to fill in those gaps?

If chimps have 24 chromosomes and humans have 23, that implies 2 chromosomes have fused in humans. This fusion would put telomeric DNA in the middle of a human chromosome, not an ape/chimp chromosome.

Depends, there are several sequencing technologies and they all have strengths/weaknesses. At my job, we use 454 sequencing from Roche and since it relies on PCR it has problems with tandem repeats and homopolymers that might not trip up other methods. (Sanger for example)

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