If you really want to double-check the work, you will need to go to the place where the cores are archived, borrow a microscope and re-read them yourself. It makes little sense to say that somebody made a mistake in analysis, then trust that same person to have read the cores correctly. Most reading mistakes can be detected using correlation or pointer analysis using the data at hand. Often, the exact year that is misread can be determined. If you find such a mistake, the easy solution to the problem is to delete that one reading from the dataset. As there are cracks, knots, hazel marks, fire scars and other defects in cores, it is routine to delete readings that can't be made accurately. You won't usually find that kind of mistake, though because the author will have run the tests himself.
If all else fails, take an increment borer and go to the place where the cores were collected and make your own collection. It is polite to get permission from the owner first, but I know of one collection that the National Park Service still hasn't found out about. If you have gone to all the trouble to make your own collection, you have something that you can publish, so work it up and publish it.
Many dendro publications are beginning to insist that ownership of datasets be turned over to them prior to publication. They then make the dataset available to anyone who wants it, usually for a fee. This allows readers to re-run analyses they are suspicious of.
P.S.: If you make your own collection, take an extra increment borer. A broken bit can be a disaster - take it from an experienced hand at core collecting.