Ég skoða launaseðilinn minn alltaf vandlega, því stundum er eitthvað rangt.

Not quite. Skoða usually means look at, examine, inspect, or check. It is more active than simply see.

So in this sentence, Ég skoða launaseðilinn minn... means something like I check / inspect my payslip..., not just I happen to see my payslip.

A useful contrast is:

• sjá = see
• skoða = look at carefully / examine

Because Icelandic loves compound nouns.

Launaseðilinn is built from:

• laun = wages / salary
• seðill = slip / note
• -inn = the attached to the end

So:

• launaseðill = payslip
• launaseðilinn = the payslip

This is very normal in Icelandic. English often uses separate words where Icelandic prefers one compound word.

Two things are happening:

1. The noun is definite: the payslip
2. It is the direct object of skoða, so it is in the accusative

The dictionary form is:

• launaseðill = payslip

But after a verb like skoða, it appears in the accusative singular:

• launaseðil

Then the definite ending is added:

• launaseðilinn = the payslip

So the form reflects both case and definiteness.

In Icelandic, possessives are very often placed after the noun, especially when the noun is definite.

So:

• launaseðilinn minn = my payslip

This is a very natural pattern in Icelandic:

• bíllinn minn = my car
• húsið mitt = my house

You can sometimes put the possessive before the noun, but that usually sounds more emphatic, literary, or contrastive, and the structure changes.

Because minn has to agree with the noun it belongs to.

Launaseðill is a masculine singular noun, so the possessive must match that. Here the matching form is minn.

Compare:

• masculine: bíllinn minn = my car
• feminine: bókin mín = my book
• neuter: húsið mitt = my house

So minn is used because launaseðill is masculine.

They are both adverbs, but they do different jobs:

• alltaf = always
  This tells you how often
• vandlega = carefully / thoroughly
  This tells you how

So:

• Ég skoða launaseðilinn minn alltaf vandlega
  = I always check my payslip carefully

One adverb gives frequency, the other gives manner.

The order is not completely fixed, but the given order is very natural.

Alltaf often comes before vandlega because always is a frequency adverb and carefully is a manner adverb. That feels natural in Icelandic, just as it often does in English.

You may also hear slightly different placements, for example:

• Ég skoða alltaf launaseðilinn minn vandlega.

That is also natural. But the exact placement can slightly change emphasis.

So the sentence you were given is normal and idiomatic, not the only possible order.

Here því means because or for, introducing the reason for the first statement.

So:

• ... því stundum er eitthvað rangt.
• ... because sometimes something is wrong.

A very common fuller alternative is af því að, which also means because:

• Ég skoða launaseðilinn minn alltaf vandlega, af því að stundum er eitthvað rangt.

That version may sound a little more explicit or conversational.

Because the sentence has two clauses:

• Ég skoða launaseðilinn minn alltaf vandlega
• því stundum er eitthvað rangt

In standard Icelandic writing, a comma is often used to separate clauses, especially when the second clause gives a reason or explanation. So the comma here is normal.

Eitthvað means something.

In this sentence:

• stundum er eitthvað rangt
• sometimes something is wrong

It is an indefinite pronoun, used when you are not naming exactly what the problem is. You are just saying that something on the payslip may be incorrect.

Because rangt agrees with eitthvað, and eitthvað is neuter singular.

Icelandic adjectives change form to match the word they describe or refer to. Here the adjective is being used predicatively after er:

• eitthvað er rangt = something is wrong

Since eitthvað is neuter singular, the adjective must also be neuter singular:

• masculine: rangur
• feminine: röng
• neuter: rangt

That is why rangt is the correct form here.

Because stundum is being given a prominent position: sometimes.

Starting the clause with stundum highlights the idea that the problem does not happen all the time, only on some occasions:

• því stundum er eitthvað rangt
  = because sometimes something is wrong

Icelandic often puts an adverb first in a clause for emphasis or natural flow. So this word order is perfectly normal.

The letter þ is pronounced like the th in thin, thing, or thank.

So því starts with that same sound, not with a t or z sound.

A rough English approximation of því is:

• thvee

It will not be exact, but it is a useful starting point.