Такие ошибки часто встречаются в тексте.

Because такие has to agree with ошибки in number, gender, and case.

• ошибки here is plural
• in this sentence it is in the nominative plural
• so the demonstrative adjective must also be nominative plural

That gives:

• такой — masculine singular
• такая — feminine singular
• такое — neuter singular
• такие — plural

Since ошибки = errors/mistakes is plural, такие ошибки means such errors / mistakes like these.

Because ошибки is the subject of the sentence.

The basic structure is:

• Такие ошибки = such mistakes
• часто встречаются = often occur / are often found
• в тексте = in the text

So the sentence is literally structured like:

Such mistakes often occur in the text.

Since the subject is plural, it appears in the nominative plural: ошибки.

Because it agrees with the subject ошибки, which is plural.

Russian verbs in the present tense agree with the subject in number (and in the past tense also in gender).

Compare:

• Ошибка встречается в тексте. = Such an error occurs in the text.
• Ошибки встречаются в тексте. = Errors occur in the text.

So with plural ошибки, you need plural встречаются.

That is a very common question. In this sentence, встречаться does not mean to meet someone in the usual social sense.

Here встречаться means:

• to occur
• to appear
• to be found
• to be encountered

So Такие ошибки часто встречаются в тексте means something like:

• Such mistakes often occur in the text
• Such mistakes are often found in the text

Russian often uses встречаться this way when talking about things that appear in books, articles, speech, nature, data, and so on.

Examples:

• Это слово часто встречается в статье. = This word often occurs in the article.
• Такие случаи редко встречаются. = Such cases are rare.

The -ся ending makes the verb reflexive, but reflexive verbs in Russian do not always translate as true reflexives in English.

Here:

• встречать = to meet, to encounter
• встречаться = to meet each other / to occur / to be found, depending on context

In this sentence, встречаются has the meaning are encountered / occur.

So you should learn this as a standard usage:

• что-то встречается где-то = something occurs / is found somewhere

It is not literally reflexive in English, but grammatically it is a reflexive verb in Russian.

Because after в when it means in, Russian usually uses the prepositional case.

• текст = text
• в тексте = in the text

So:

• в + prepositional for location: in/at
• в + accusative usually for motion into something

Compare:

• в тексте = in the text
• в текст = into the text

Here there is no movement, only location, so в тексте is correct.

Usually такие ошибки is better understood as such mistakes rather than these mistakes.

Why?

Because такой often means:

• such
• this kind of
• like that / like this

So такие ошибки suggests a type of mistake, not necessarily a specific set of mistakes right in front of you.

If you specifically meant these mistakes, Russian would more naturally use:

• эти ошибки

So:

• такие ошибки = such mistakes / mistakes of this kind
• эти ошибки = these mistakes

That is the most neutral word order here.

• часто = often
• встречаются = occur / are found

So часто встречаются = often occur

Russian word order is flexible, so other orders are possible:

• Такие ошибки часто встречаются в тексте.
• В тексте такие ошибки часто встречаются.
• Такие ошибки в тексте часто встречаются.

These all mean roughly the same thing, but the emphasis changes a little.

The original version sounds natural and neutral.

Yes, it is grammatically possible, but it sounds a little less neutral.

Russian adverbs like часто can move around, but their position affects rhythm and emphasis.

Compare:

• Такие ошибки часто встречаются в тексте. — neutral, natural
• Такие ошибки встречаются часто в тексте. — possible, but часто gets a bit more emphasis

A native speaker would usually prefer the original order unless there is a special reason to stress often.

Встречаются is imperfective.

That matters because the sentence describes something that happens generally, repeatedly, or typically:

• such mistakes often occur

Russian uses the imperfective for habitual or repeated actions.

The perfective partner is usually встретиться, but that would not fit here in the same way, because perfective verbs are about a completed event.

So for a general statement like this, встречаются is exactly what you want.

Yes. Depending on style, you might also hear:

• попадаются — are encountered, turn up
• бывают — happen, occur
• появляются — appear
• содержатся — are contained

But each has a slightly different nuance.

For example:

• Такие ошибки часто встречаются в тексте.
  = Such mistakes often occur in the text.

• В тексте часто попадаются такие ошибки.
  = You often come across such mistakes in the text.

• В тексте часто бывают такие ошибки.
  = Such mistakes often happen in the text.

Встречаются is a very natural and common choice here.

It has a normal subject: такие ошибки.

Even though English often uses passive-like translations such as are found, the Russian sentence is not impersonal. It is a regular sentence where:

• такие ошибки = subject
• встречаются = verb
• в тексте = location

So grammatically it is straightforward: Such mistakes often occur in the text.

The singular version would be:

Такая ошибка часто встречается в тексте.

Changes:

• такие → такая because ошибка is feminine singular
• ошибки → ошибка
• встречаются → встречается to match the singular subject

So:

• Такая ошибка часто встречается в тексте.
• Такие ошибки часто встречаются в тексте.

This is a useful pattern to remember.