Hun er grundig, og desuden er hun opmærksom på små fejl.

Because grundig is a predicate adjective after er, and it agrees with the subject.

• hun = common gender singular, so the adjective stays in its base form: Hun er grundig
• with a neuter subject, you would usually get -t: Det er grundigt
• with a plural subject, you usually get -e: De er grundige

So here grundig is the correct form because the subject is hun.

Desuden means something like besides, furthermore, or in addition.

So:

• og simply links the two parts
• desuden adds the idea that the second quality is an extra positive point

Without desuden, the sentence would still be correct:

Hun er grundig, og hun er opmærksom på små fejl.

But desuden makes it sound a bit more structured and a little more formal or polished.

Because Danish main clauses follow the V2 rule: the finite verb normally comes in the second position.

In the second clause, desuden has been placed first. When something other than the subject comes first, the verb must come next:

• Desuden er hun opmærksom ...

Not:

• Desuden hun er ...

This is very common in Danish:

• I dag kommer han.
• Derfor er vi glade.
• Desuden er hun opmærksom ...

Because the sentence contains two coordinated main clauses, and each clause needs its own subject.

• Hun er grundig
• og desuden er hun opmærksom på små fejl

You cannot leave out hun in that structure.

However, you could restructure the sentence as one clause with two descriptions:

Hun er grundig og opmærksom på små fejl.

That is also correct, but it does not have exactly the same emphasis as the original sentence.

Yes, basically. Opmærksom på is a fixed combination.

It means attentive to, alert to, or aware of something.

So you say:

• opmærksom på detaljer
• opmærksom på problemer
• opmærksom på små fejl

This is one of those adjective + preposition combinations that learners usually need to memorize as a unit.

Because små is the form used with plural nouns.

The singular form is lille:

• en lille fejl = one small mistake

But with a plural noun, you use små:

• små fejl = small mistakes

So:

• singular: en lille fejl
• plural: små fejl

This is an irregular pattern, so it is worth learning separately.

Here it is plural.

The noun fejl is one of those Danish nouns whose singular and plural forms are often the same in writing:

• singular: en fejl
• plural: fejl

In this sentence, we know it is plural because of små:

• små fejl = small mistakes

If it were singular, you would expect something like:

• en lille fejl

Yes. Danish allows some flexibility with adverbs like desuden.

For example, these are also possible:

• Hun er grundig, og hun er desuden opmærksom på små fejl.
• Hun er grundig og desuden opmærksom på små fejl.

The original version:

• Hun er grundig, og desuden er hun opmærksom på små fejl.

puts extra focus on desuden by placing it first in the second clause.

It is fairly neutral, but it often sounds a bit more written, careful, or formal than very everyday alternatives.

Depending on context, spoken Danish might also use things like:

• også = also
• derudover = in addition
• ovenikøbet = on top of that / even

So desuden is completely natural, but it has a slightly polished tone.

Because the sentence joins two independent clauses:

• Hun er grundig
• desuden er hun opmærksom på små fejl

In standard Danish punctuation, a comma is normally used here when og links two full clauses with their own verbs.

So the comma helps show the structure clearly.