I was reading an article in The Independent (an interview of a native English speaker) and I read the following sentence:
We travelled across by the boat to Mljet National Park . . .
Shouldn't we say "by boat" instead ?
We travelled across by boat, by train, and so forth, with no article, is usual when you are speaking merely of the mode of transport you are using. It is equivalent to We took a boat, a train, and so forth.
By the boat, the train, and so forth imply a particular boat or train—usually ‘the’ regularly scheduled boat or train or whatever to that particular destination.
This is probably why Ms. Coleman speaks of “the boat to Mljet National Park”. As Vic suggests, we would ordinarily keep across to together if we were speaking of the park as our destination; but Ms. Coleman is probably using “to Mljet National Park” to distinguish which boat: the one which goes to that park as opposed to other boats which go to other locations on the island, or to other islands.
There is nothing specifically wrong with that statement.
"by boat" vs "by the boat":
Using "by the boat" implies that there is an alternative to the boat for crossing, such as a bridge.
That's not the only mistake. The correct way to write it would be:
Adverbs of manner go before the main verb, after the auxiliary verb or at the end of the sentence. When there are two or more adverbs in the same sentence and there is a verb of movement, such as "go", "come", "leave", travel", then the adverbs come in the following order: place-manner-time
I know that this was not what you are asking about, but there were two mistakes.
As for "By boat", there's nothing to explain; we always say."by boat","by bus", "by train",etc.