Well, the short and simple answer that we have is that Milo Rambaldi had a fascination with the number 47. Therefore all Rambadli-related things naturally have 47 worked in. The machine in the Telling had 47 parts, the prophecy was on the 47th page. Syd dreamed about walking into room 47 likely because before her memory was wiped, she was eyeball deep in Rambaldi stuff and some part of her mind remembered that.
On the broader scope, you are also correct that 47 shows up a lot in the show. Some examples of where it occurs is in the number of Euros Dixon collects while under cover in an airport, part of an ID number, part of a security code, someone even once told me the full Alias intro from Seasons I and II takes 47 seconds... My personal suspicion is that this is JJ's way of hinting that just like the number 47, Rambaldi is threading through and underlying much of the plotlines and story arcs.