Thank you SoSick for these good questions.

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how exactly do they count tree rings accurately without cutting the tree down anyway? it would have to be an estimate, not an actual ring count.
They take a core sample. Actually they take several samples to compare for consistent counts. See this picture for a core and try this wiki link for a picture of a core drill and some further information.

Also see Paleo Slide Set: Tree Rings: Ancient Chronicles of Environmental Change for more information and see this page for some basics
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Various factors can add more than one ring per year also. Bex found some info about that.
The question is not whether there can be extra rings or missing rings - there can, because we are dealing with natural living organisms in a variable environment - the question is whether we can identify when this happens and be able to correct the data. The slide show talks about how that is done in a fairly simple format.

The article that Bex was talking about is likely this one by Don Batten where he states:
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... the plantation pine Pinus radiata, has revealed that up to five rings per year can be produced ...
I only need to note these things:
  • he was able to identify all five rings as being false rings without any problem,
  • if he was making a chronology he could deduct 5 years from this tree,
  • he doesn't tell you about missing or partial rings, rings that don't grow for the year in question, or that are incomplete (say from a summer on a mountain top being too cold for growth) and which may be missed by the core, and which would make the trees too young if this effect was not determined,
  • he doesn't tell you how he determined the missing rings, or provide any data from this "research", or a link to where the information could be found, so we also don't know what the %error would be involved if these were counted in error,
  • dendrochronology uses multiple cores from multiple trees from multiple sites to build up a chronology rather than rely on one tree, and reduce these uncertainties and finally
  • he uses intentional mis-direction (remember the "Russ Tanner Manifesto Lie Test"?) to talk about a completely different species - in an entirely different subgenus, that grows in a completely different environment, and that has been bred for fast growth by the forest industry - with the stated implication that they are the same tree. This is the hallmark of a scam, a con and a fraud . The genus Pinus - which includes all pine trees - includes some 115 different species in three subgenus divisions: Strobus (white or soft pines), Ducampopinus (pinyon, lacebark and bristlecone pines) and Pinus (yellow or hard pines)[6]. The Monterey Pine is in the subgenus Pinus[4], while the Bristlecone Pines are in the subgenus Ducampopinus.
(See Dendrochronolgy Fact and Creationist Fraud for a more complete critique of the lies of Don Batten.)

Once again I need to ask, if creationism is true, then why do creationists (like Don Batten) need to lie about the facts?
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the forest service claims there are lots of trees that old, some older than that. why would they protect that one?
Because it is the oldest living organism they know of (& that can be dated), tree, mushroom, coral, whatever, and because one other that was older was cut down and a lot of people were upset and blamed them for being lax and careless. Personally it doesn't make much difference, because a tree cannot grow further into the past, no matter how old it is.

The older tree was the "Prometheus Tree":
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Prometheus (aka WPN-114) is the nickname given to the oldest non-clonal organism ever known, a Great Basin Bristlecone Pine (Pinus longaeva) tree about 4900 years old growing at treeline on a mountain in eastern Nevada, USA. The tree was cut down on August 6, 1964 by a graduate student and U.S. Forest Service personnel for research purposes, though at the time they did not know of its world-record age. The cutting of the tree remains controversial.
From this article on Bristlecone Pine information:
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The oldest known living specimen is the "Methuselah" tree, sampled by Schulman and Harlan in the White Mountains of CA, for which 4,789 years are verified by crossdating. An age of 4,844 years was determined post-mortem (after being cut down) for specimen WPM-114 from Wheeler Peak, NV. The age is largely crossdated (6). Naturally, these ages underestimate the true ages of the respective trees (see Tree Age Determination for details), perhaps by hundreds of years in view of the fact that pith dates were not recovered for these trees. It seems likely that trees at least 5000 years old exist.
With an age of 4,789 years in 1964 when the tree was cut down this means that "Prometheus" or WPM-114 has an estimated germination date of 2,880 BCE, just a little bit older than "Methuselah" (estimated germination 2,832 BCE). This is substantiating evidence for this age, and we will get to correlations between these trees in greater detail later in this discussion.

Enjoy

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