What percentage of a Neanderthal's DNA could be in a Denisovan?
You should be very careful trying to conclude something from what is known about Neandertal genetics.

To answer question 1: NO! This is probably not what he meant. To date, we have only two high-quality full genomes of archaich humans, one being the (Neandertal from Denisova cave, called Altai Neandertal (Prüfer et al., 2014)) and one being the (Denisovan from Denisova cave (Meyer et. al., 2012)). From this sample (which is exactly one Neandertal) you cannot draw conclusion for the whole population. It seems, however, that this Neandertal individual from the Altai Mountains was indeed inbreed (high runs of homozygosity in the genome) - it does, however, not even tell us in what way her parents were related. Prüfer et al. (2014) write


  We conclude that the parents of this Neandertal individual were either half-siblings who had a mother in common, double first cousins, an uncle and a niece, an aunt and a nephew, a grandfather and a granddaughter, or a grandmother and a grandson.


You cannot say more. You also cannot say if this was due to preference in mate choice, or caused by the fact that this group was very isolated, or  that this population had an extreme small effective population size (note that it is debated whether the last two effects are actually equivalent).
To make a long story short: based on the available data it is not wise to draw general conlcusions about Neandertal mating behaviour. Altai is the only example where direct inbreeding could be shown, all other genetic data from Neandertals suggest that genetic diversity was just low.

To answer question 2: I do not really know what this means, 70% Neandertal DNA in Densiovans. I can just generally tell you something about Densiovan-Neandertal differences. The Densiovan might be the only (at least mammal) species that was defined based on genetic information alone. Alle that was found were a few teeth and a pinky bone. People thought this was another Neandertal. After sequencing the DNA from that bones to high coverage (vaguely, a measure of qualtiy), one found that the DNA falls both outside the variation of modern humans - showing that this was not a Homo sapiens, but interestingly it also clearly falls outside the variation of known Neandertal sequences - showing that this was not a Neandertal. It also became clear that Densiovans are more closely related to Neandertals than to modern humans (you might now ask yourself how this is possible with just one genome. In fact, there are more genetic data availabe: low coverage genomes, exome sequences, mtDNA and all of them show the same thing: Neandertals and Densiovans are different but more closely related to each other than to modern humans). Overall, Denisovans also seem to have had rather low genetic diversity (which by the way is also a characteristic of modern humans).
Long story short: There seem to have been admixture events between Denisovans and Neandertals but I do not know how to relate this to the 70%. Prüfer et al. (2014) detected about 0.5% contribution from Neandertals in Denisovans.

One last comment about this mysterious species (nobody says it but most people think of Homo erectus): again, Prüfer et al. (2014) found some interesting patterns of derived allele sharing between present-day Africans, Denisovans and Neandertals (this should be equal for African-Denisovan and African-Neandertal comparisons, but present-day Africans share about 7% more derived alleles with Neandertals than with Densiovans - even 13-16% in alleles fixed in present-day Africans). This is either ancient population structure (however, with very deep lineages) or, as suggested in the paper, due to gene flow from a (genetically) unknown archaic hominin into Denisovans. 

I hope this clears things up a bit. Feel free to ask in the comment and I will edit the post as it might be a bit unstructured.