I think the literal English equivalent would be:
Let one thing be said (to you).
"Let one thing be clear."
Sei, in this instance, is formally third person singular present subjunctive. The meaning is that of an optative, i.e. a wish. The same could be expressed periphrastically with sollen.
Eins soll dir gesagt sein.
The construction seems like run-of-the-mill German to me. Further examples:
Eins sei nicht vergessen. / Eins soll nicht vergessen sein.
Let one thing not be forgotten.
"Let's not forget one thing."
Nur so viel sei verraten. / Nur so viel soll verraten sein.
Let only this much be revealed.
"We'll only reveal this much."
Die wichtigsten Punkte seien noch einmal wiederholt.
Let the most important points be reiterated.
"Let's reiterate the most important points."
For another example where English has let and German a subjunctive, see Genesis 1:3:
Let there be light!
Es werde Licht!
To see that sei is not imperative in the above examples, compare a case where it is:
Sei gewiß, daß nichts dein Eigentum sei, was du nicht inwendig in dir hast. (Matthias Claudius)
Rest assured that nothing is your property that you do not have within you.
Note that the verb is in first position and that the unrealized subject is the addressee (you rest assured), whereas in the subjunctive examples, the verb occurs in second position and the subject is overtly realized, not a person and not the addressee.
The song is in Standard German. The lenition of the internal consonant and shortening of the stressed vowel of Vater – going from [ˈfaːtɐ] to [ˈfad̥ɐ] – is widespread in northern colloquial German. The only other obvious deviations from Standard German I could spot are the diphthongization of the vowel in schon right at the beginning and the form Jung (tending towards Jong) instead of Jungen (2:48).