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Unstable like how much? "prone to cancer", or unstable like "physical destruction due to DNA helixes ripped apart"?

The former, though likely still at a pretty low rate. These instabilities can result in mis-pairing at replication which results in a mutation in the replicated strand. Article suggests that this may be a significant source of mutations that was previously not considered.

Article says: We find it to be several orders of magnitude greater than the observed rate (10−8 per base pair) of spontaneous mutations through, for example, copying errors, suggesting that tautomerisation may well play an important role in point mutations.

The article suggests that it is a minor cause of point mutations.

Yes, I've been scouring TFA but what I wish to learn is:

What is the practical outcome of experiencing / accumulating said mutations?

In the vast majority of cases, nothing, as the mutations will likely be silent. In the worst case, a point mutation could possible lead to the development of a cancer. But remember, the article says this has been going on all the time as natural process. It's not new. So no increased risk from this process.

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