Related to this: Death note handwriting check
A lot of DNA must have rubbed off on the Death Notes. Unless the Death Note has a rule about fingerprints or DNA, I don't see how this isn't a plothole.
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Since my answer at the linked question answers this question as well, I will only copy it in a quote:
After handing over the Death Note to Rem in the plan to free Misa out Light says (chapter 54):
In other words, he tore the pages out and checked there's none of the fingerprints or his handwriting, so it's no surprise that L didn't check out the handwriting since there weren't any other names written beside Higuchi's.
All though it didn't mentioned in the anime, it's unthinkable that Light would missing do such an obvious thing.
And as for hair and DNA as mentioned in the question, I think it's obviously.
When the Kira Task Force recovered the Death Note from Kyosuke Higuchi there is 2 things which contaminated any DNA evidence on the Death Note:
To my knowledge there is no way to tell "when" fingerprints or DNA first made contact with an object being tested as such any of Light's DNA found on the Death Note can easily be explained by his interactions with it when the Death Note was recovered.
Remember that the idea was to capture Kira and convict him in a court of law and DNA on the Death Note would be inadmissible due to how it was handled. This is why the police tend to block of crime scenes ensure that the proper Chain of Evidence is met. In some cop shows there are times that, when a seal is broken or multiple undocumented people handled a particular piece of evidence, it can't be used in court.
Even if Light didn't touch the Death Note when it was recovered and L found Light's DNA on it, suspecting Light again after the 13-day rule seemed to show his innocence would not help L since up until now Light had been very cooperative in aiding the Task Force and they were all on good terms. He would first need to prove to the rest of the Task Force/Police that the 13-day rule is fake thus returning to what I have explained here and then rule out any other way Light's DNA could have gotten onto the Death Note after it's recovery.
This is just a plothole. People can argue that Kira can rip off pages etc, but he was touching the cover as well. Also the fact that L and Light already touched death note after recovering it doesnt expain it neither for 3 reasons:
1.) every evidance can be secured and L being detective as brilliant as he is, should know that touching an evidence can ruin it.
2.) even if L and Light touched the Death Note, the only reason they would abandoned the idea of taking fingerprints is assumption than Light is Kira so there's no reason to take fingerprints. Without assuming it, they should still take fingerprints - in case of them fidning a fingerprints that don't belong to anyone from the task force, they could assume this fingerprints are a proof (they wouldn't find anything substantial, but they dont know it until they don't check it).
3.) Even if it cant be used as proof, there's no reason for L not to check for them. He could find out something interesting about Kira - maybe for example if he was right or left-handed? Something helpful, a clue, that can lead to finding real evidence.
4.) even if the Ddath Note has be already touched, they can run test to figure out that there's only task force and the fake kira tt have been touching death note, which is very suspecious.
In the end of the day it's just a plot hole, there's no perfect explanation for it, it just something that happen even in best written stories.