Living Fossils cause a problem for the Fossil Record because no evidence is found in the in between layers. Example: The coelacanth fish. It is found in the Devonian period layer and found alive today. Yet it is not found in any other layer above where it was found showing it survive to this point and time. That is 7 layers it is missing from.
Appearing in the other layers would prove they survived and did not change. That is if the fossil record is correct in supporting evolution. What we would expect to find, if the fossil record does not support evolution, is no record of living fossils surviving until present time.
Example: Claiming that the fossil record is accurate even though it does not support living fossils surviving until present time. Would be like saying a big gap in time in your family tree means the records were accurate. It just does not work in supporting evolution.
If you would like to do more research on this, here is a list of living fossils: http://en.wikipedia.org/wiki/Living_fossil You can look each one up yourself then ponder why not one is found in any other layer. An accurate record of time would show living fossils surviving. That is if evolution were true.