It's very easy to discover short features (substantially shorter than read length, like a 20bp indel for 150bp reads) with very low depth sequencing (say, 3x) with some degree of certainty. In that case, more coverage simply buys more confidence. Heterozygous features on a diploid require more coverage than homozygous features, of course. But the coverage needed is a function of the read length, error rate, sequencing methodology (paired or unpaired? insert size distribution?), what you're looking for (novel or well-known variants?), genome type (complexity and repetitiveness), biases present in sequencing, and so forth. I have not read the paper, but to make any claim of a specific level of coverage required, these factors need to be specified along with a given level of confidence desired. I've called short heterozygous variations with low (<10x) coverage using short, high-error-rate, highly-biased 50bp colorspace reads. The confidence level can be quite good even in that very undesirable case (>95% accuracy), as determined by sequencing trios. Generally, though, I don't recommend it. However, with high-quality 2x250bp reads using methodology which incurs little bias, you could get extremely high confidence het calls with coverage much substantially lower than 35x.
There is a difference, though, between claiming a single variant is a high-confidence real heterozygous variant (which can be done at 10x) and that you have, with high confidence, found virtually all real heterozygous variants and correctly classified them as heterozygous. The latter can't be done at 10x regardless of your methods (for bulk-DNA shotgun sequencing), because best-case scenario, there's still a 1/512 chance that all reads covering a given location came from the same chromosome copy (that's (1/2^10)*2)).
Features similar to or longer than read length, such as long insertions and other structural variations, need to be implied by coverage rather than called within a single read, though. So they are more coverage-dependent.
Tagging i.sudbery