Who were the Kohanim to whom the Pasuk is referring?
Rashi and Rashbam: The Bechoros, who performed the Avodah until Aharon and his sons were chosen.
Hadar Zekenim: It is the descendants of Aharon (refer to 19:22:151:1).
Why might they think that they are permitted to ascend the mountain?
Rashi: Because they already come close to Hashem when they bring Korbanos to Him.
Why does it say here "Pen Yifrotz Bahem"? Pasuk 24 says "Pen Yifrotz Bam"!
Hadar Zekenim (20): The extra Hei alludes to five Kohanim who were punished
In this verse with the Hei, Kohanim are mentioned closest to Yifrotz. This seems to be the intent of Hadar Zekenim. (PF)