Learn Hardcore Japanese: tomodati ga kaita meeru ni ha tiisana matigai ga ookatta. - The email my friend wrote had many small mistakes.

に marks the location or target (here “in the email”), and は turns that phrase into the topic/emphasis. Using メールには means “as for in the email…” to highlight that context.

Just メールに would simply mark location without topical emphasis.
Just メールは would shift focus to the email itself, not specifically to what’s inside it.

Why is 書いた in the past tense when modifying メール? Could we use 書くメール instead?

In Japanese relative clauses, the tense reflects when the action occurred relative to the main clause.

書いたメール means “the email that my friend wrote” – the writing is completed before we talk about its mistakes.
書くメール would imply a future or habitual action (“emails he will write” or “the kinds of emails he writes”), which isn’t what we mean here.

Why are there two が particles in 友達が書いたメールには小さな間違いが多かった?

They mark two different subjects:

友達が marks “my friend” as the subject of the verb 書いた.
間違いが marks “mistakes” as the subject of the adjective 多かった (“were many”).

Why is 間違い marked with が before 多かった, instead of putting the particle on メール?

Because the thing that is “many” is 間違い (mistakes), not メール (the email). In Japanese you mark the actual subject of the predicate with が, so you say literally “mistakes were many,” while メール is just the topic or location.

Why is 小さな used instead of 小さい in 小さな間違い? Could I say 小さい間違い?

Both are possible:

小さな is a prenominal (na-type) adjective used directly before nouns, often adding a slightly softer or literary nuance.
小さい間違い (using the i-adjective) is more common in everyday speech and equally natural. Choice is mostly stylistic.

Why is there no を after 書いた to mark メール? Shouldn’t we have 友達がメールを書いた?

When a verb phrase directly modifies a noun (forming a relative clause), Japanese typically omits the object marker を before that noun. So 友達が書いたメール (“the email [that] my friend wrote”) is standard.

Why is 多かった (past form) used instead of 多い (present)? Could I say 多い?

Using 多かった places the statement in the past, fitting the idea that you examined that specific email and found many mistakes.

多い could work if you’re making a general, timeless statement about such emails, but for that particular email (a completed context), past tense sounds more natural.

Could I omit the は in メールには and say メールに小さな間違いが多かった? Would that change the meaning?

Yes, you can.

メールに小さな間違いが多かった is still grammatical and simply descriptive (“in the email there were many small mistakes”).
Adding は (メールには) gives you a bit more contrast or emphasis on “in that email” as the topic.

Could I use メールでは instead of メールには? What’s the difference?

Yes, メールでは (“in/at the email …”) is grammatically fine.

では marks location neutrally.
には (combining に
- topical は) puts extra emphasis on “as for inside that email,” making it clearer you’re contrasting or focusing on that context.