Если Вы заметите какие-либо ошибки, скажите мне, пожалуйста.

Capitalized Вы is a polite, formal way to write you when addressing one person respectfully.

So in this sentence:

• Вы = formal singular you
• заметите and скажите are also in the plural/formal form, which matches Вы

In modern Russian, writing Вы with a capital letter is common in formal letters, emails, and polite written communication. In less formal writing, you may also see вы with a lowercase letter.

Because Russian usually uses the perfective verb in this kind of future condition.

• заметить = to notice, to spot once, successfully
• замечать = to notice regularly, habitually, or as an ongoing process

Here the meaning is:

• If you happen to notice...
• If you do notice...

So заметите is the natural choice, because it refers to a single completed future event.

This is a very common Russian feature.

заметить is a perfective verb. Perfective verbs do not have a true present tense. Their so-called present forms actually refer to the future.

So:

• я замечаю = I notice / I am noticing (imperfective, present)
• я замечу = I will notice (perfective, future)

Therefore:

• Если Вы заметите... = If you notice / if you will notice...

In English we usually say if you notice, not if you will notice, but the Russian form is still future in meaning.

Because Если Вы заметите какие-либо ошибки is a subordinate if-clause, and Russian separates it from the main clause with a comma.

Structure:

• Если Вы заметите какие-либо ошибки, = If you notice any errors,
• скажите мне, пожалуйста. = please tell me.

This comma is required in standard Russian punctuation.

Какие-либо means any, any whatsoever, or any kind of in a rather formal or neutral written style.

So:

• какие-либо ошибки = any errors

This fits well after если.

Compare:

• какие-либо = any, any at all; often formal/written
• какие-нибудь = any, some or other; very common in everyday speech
• какие-то = some (unspecified), often implying some particular but unidentified ones

In this sentence, какие-либо ошибки sounds natural and polite, especially in writing.
A more conversational version could be:

• Если Вы заметите какие-нибудь ошибки...

Because ошибки here is the accusative plural of an inanimate noun, and for inanimate plural nouns, the accusative looks the same as the nominative.

Singular:

• nominative: ошибка
• accusative: ошибку

Plural:

• nominative: ошибки
• accusative: ошибки

Since заметить takes a direct object, ошибки is in the accusative, even though it looks identical to the nominative plural.

Because сказать means to say / to tell as a single completed act, while говорить usually means to speak / to say in a more ongoing or repeated sense.

Here the speaker wants one specific action:

• If you notice any errors, tell me.

So the perfective imperative скажите is the natural choice.

Compare:

• скажите мне = tell me / let me know
• говорите = speak, go ahead and speak, keep talking

In this context, говорите мне would sound unnatural.

Because сказать often takes the pattern:

• сказать кому? что? = to tell someone something

So:

• мне = to me / me (dative)
• сказать мне = tell me

This is just the regular case pattern of the verb.

Пожалуйста makes the request polite. In this sentence it works like please.

So:

• скажите мне = tell me
• скажите мне, пожалуйста = please tell me

Russian пожалуйста is very flexible in position, but here it is placed naturally after the request. The commas around it are standard.

Because the imperative for Вы uses the same plural/formal pattern.

Russian uses the same verb agreement for:

• you all
• formal you to one person

So:

• скажи = tell (one person, informal ты)
• скажите = tell (plural or formal Вы)

Since the sentence uses formal Вы, скажите is exactly what we expect.

Yes. Russian word order is fairly flexible.

This sentence:

• Если Вы заметите какие-либо ошибки, скажите мне, пожалуйста.

could also be rearranged, for example:

• Скажите мне, пожалуйста, если Вы заметите какие-либо ошибки.

Both mean essentially the same thing. The original version is very natural because it presents the condition first, then the request.

It is definitely on the polite/formal side.

Reasons:

• Вы instead of ты
• скажите instead of скажи
• какие-либо sounds somewhat formal/written
• пожалуйста adds politeness

A more informal version to a friend would be:

• Если заметишь какие-нибудь ошибки, скажи мне, пожалуйста.

Yes. You can say:

• Если Вы заметите ошибки, скажите мне, пожалуйста.

This is still correct and natural.
Adding какие-либо just makes the meaning more explicitly any errors at all and gives the sentence a slightly more formal tone.

So:

• заметите ошибки = notice errors
• заметите какие-либо ошибки = notice any errors whatsoever

Both work; the version with какие-либо is a bit more careful and polished.