Rios mentions that his former Captain Alonzo Vandermeer had served as 1st Officer under Captain Marta Batanides. In Tapestry (1993), Marta was shown to be a former classmate and old flame of Jean-Luc Picard.
Picard talks about being an ensign on the USS Reliant (obviously not the ship from Star Trek II: The Wrath of Khan (1982), as that was destroyed) in the extended cut of The Measure of a Man (1989). Picard and Admiral Nakamura talk about serving on "the old Reliant;" this episode makes it canon.
According to the English subtitles, Ian/Iain says: "He's sae fou as a piper, an' awfu aff the fang". 'Fou' appears in a number of old Scottish poems and means drunk, as in Robert Burns' 'Tam O'Shanter': "Tam lo'ed him like a vera brither; They had been fou for weeks thegither." (Tam loved him like a very brother; They had been drunk for weeks together.")
Here, the idom means, "he's as drunk as a piper " (piper=someone who plays the bagpipes, not noted for sobriety). 'Fou' is from the French 'fou' ('crazy'), not 'fu', a Scottish contraction of 'full'. The idiom is now archaic and even the more modern versions, 'fou as a puggie/whulk' ('drunk as a frog/whelk') are dying out.
Awfu/awful/awfy/affy is a Scots intensifier for something being very much so, e.g. "awfy wee" is "very small". "Aff the fang" is an old Scottish term that literally means having lost suction (of a pump). Figuratively, it can mean not in the mood/out of humour/without one's usual power. So, it means something like: he's as drunk as a piper and very much out of sorts.
Among the mementos in Rios's cigar box is his old Starfleet combadge. The prop department engraved the back of the badge with his name and Starfleet serial number.
The Scottish accent of the holographic engineer is likely a nod to Scotty, the engineer from Star Trek (1966).