What are "Zedim"?
Rashi: They are Mezid sins. Radak - Zed is a noun, and not an adjective. It has the same grammatical form as "Reish va'Osher" (Mishlei 30:8), "Yesh l'El Yadi" (Bereishis 31:29).
Malbim: They are intentional sinners who argue with him and deceive him via their claims.
Did David ask Hashem to guard him from Mezid sin?
Sanhedrin 107a: This was a request for forgiveness for Mezid sins in public.
Radak: David requested that his Yetzer ha'Ra not seize him. I will guard with all my strength, and You will help that the Yetzer ha'Ra not rule over me. Hashem helps one whose heart is proper, like He told Avimelech "va'Echsoch Gam Anochi Osecha me'Chato Li" (Bereishis 20:6).
Malbim: Even though I am sure that I will not transgress His Mitzvos b'Mezid, sometimes one errs via Zedim who argue with him and deceive him via their claims. Or, they rule over him and force him to veer from the good path. About the former he said "Gam mi'Zedim Chashoch Avdecha", lest I join to them. About the former he said "Al Yimshelu Vi Az Eisam" (I will be pure) "v'Nikeisei mi'Pesha Rav" - I will surely not sin b'Mezid or via rebellion.
What is the meaning of "Az Eisam"?
Rashi: [If You do so,] I will be Tamim.
Why is "Eisam" written with a Yud?
Radak: The Yud is in place of a Dagesh.
Radak citing a Drashah: The Gematriya of Yud is 10. The Torah was given via 10 Dibros; they are its purity and perfection. When You will cleanse me from Shogeg and help that Mezid not rule over me, then I will be pure and perfect.
Why did he say "v'Nikeisi mi'Pesha Rav"?
Rashi (from Shocher Tov): David was like a Kusi beggar, the ultimate schemer. First he asks for water to drink - it is for free. After, he asks for a small onion. After, he says, is there an onion without salt?! After, he says 'give to me a little bread, lest the onion harm me.' So David initially asked for Shogeg, and then Mezid, and then Pesha, which is rebellion, i.e. intent to anger - "Melech Mo'av Pasha Bi" (Melachim II, 3:7).
Sanhedrin 107a #1: David was like a Kusi merchant (who sells bit by bit; David asked for forgiveness bit by bit) "Shegi'os Mi Yavin" - Hashem forgave him for Shogeg. "Mi'Nistaros Nakeni" - Hashem forgave him for Mezid sins in private. "Gam mi'Zedim..." - Hashem forgave him for Mezid sins in public. "Al Yimshelu Vi" - Hashem consented that Chachamim will not expound his sin. "V'Nikeisi mi'Pesha Rav" (my sin should not be written in Scripture). Hashem did not grant this.
Sanhedrin 107a #2: David asked for total forgiveness [for the episode of Bas Sheva]. Hashem refused ("ha'Ba El Eshes Re'ehu Lo Yinakeh" - Mishlei 6:29) until David accepted on himself afflictions.
Radak: Zadon is when amidst desire, he sins b'Mezid. Pesha Rav is rebellion against his Master. He disgraces His Mitzvos, and transgresses even though he does not desire it. One who is used to Zadon will come to rebellion. David said, if You will cleanse me from Shogeg and help that Mezid not rule over me, if so I will never be Mezid again, and surely I will not be Poshe'a. Rav is great; the greatest of evil deeds and Aveiros is rebellion.
