Scientists think that they have counted ice layers accurately. And, they think that one layer almost always means one year. The GISP2 workers believe that they were very careful, and that they are off by less than 5% at 50,000 years BP (Before Present). But are they right?
There turn out to be a bunch of ways to check. For example, the Beryllium 10 measurements can be compared against historical records about sunspots. Unfortunately, sunspot records only go back to the invention of the telescope. Still, the records from the 1600's can indeed be matched up to the Beryllium 10 record. So, the layer counting seems correct that far back.
Another interesting measure is the element iridium. Greenland ice seems to have a lot of it in the year 1908. That probably came from the asteroid which exploded over the Tunguska River in Siberia.
Carbon dating has been applied to pollen found in various layers of the GRIP (Greenland) core. Carbon dates across the last 60,000 years were obtained, and all were in essential agreement with the matching ice-layer dates.
A radioactive dating of some ocean sediment was done, using Uranium/Thorium dating, that gave an answer of 30,470 BP plus or minus 240 years. The place in the GISP2 core which is thought to correspond, was counted as being layer 31,000. If the U/Th date is as accurate as its authors think, then the true error in that ice date is less than 2%. That's nicely within the ice date's plus or minus of 5%.
We know that there are astronomical cycles which should slowly change the climate. If the ice cores really do extend for 100,000 or 200,000 years, then the shorter astronomical cycles should have happened several times over, and some sort of cyclic effect should be detectable in the cores. This has been looked for, and found.
Erupting volcanoes give us another method. An ice layer can be analyzed to see if it contains ash, sulphur, and so on. Most layers don't. So, it should be possible to match up the volcanic layers against historical records of eruptions. And, it should be possible to match the volcanic layers in Greenland with the ones in Antarctica. It's also possible to match that against periods of bad weather, as seen by the California bristlecone pines and the Irish bog oaks. From just such tree matching, it is believed that there was a major eruption in exactly 1628 BC. That was Thera, the eruption in the Mediterranean that ended the Minoan civilization. The layers in the "Dye3" Greenland ice core say that there was a very major eruption in 1645 BC, plus or minus 20 years. So, the ice date for Thera is pretty close to the tree ring date.
That's not the only volcano, of course. Of the volcanoes that have happened in the last 2000 years, about 85% have been matched to ice layers.
Some references for the above information are:
10Be in ice at Vostok Antarctica during the last climatic cycle, Yiou et al, Nature Vol. 316 pp. 616-617, 15 August 1985
Extending the Vostok ice-core record of palaeoclimate to the penultimate glacial period, Jouzel et al, Nature Vol. 364 pp. 407-412, 29 July 1993
Irish tree rings, Santorini and volcanic dust veils, Baillie and Munro, Nature Vol. 332 pp. 344-346, 24 March 1988
The Minoan eruption of Santorini in Greece dated to 1645 BC? Hammer et al, Nature Vol. 328 pp. 517-519, 6 August 1987
Record of Volcanism Since 7000 B.C. from the GISP2 Greenland Ice Core and Implications for the Volcano-Climate System, Zielinski et al, Science Vol. 264 pp. 948-951, 13 May 1994