There are two issues here. The first issue is the "pasiva refleja" construction, which is pretty common. I already explained that to another person a few days ago, so this is nice. In Spanish passive sentences are easily formed using a reflexive form with "se" with a passive meaning, and actually that construction is more common than the usual passive with ser+participle, which is quite rare in spoken language. The pasiva refleja contruction doesn't allow the expression of the agent, though, and it's usually used when you don't want to mention who does the action. For example:
"Los albañiles construyen las casas" -"The builders build the houses"
"Las casas son construidas por los albañiles"- "The houses are built by the builders"- Passive construction with ser+participle (uncommon)
"Las casas son construidas"- Passive construction with ser+participle with no expressed agent ("the houses are built"), also uncommon
"Las casas se construyen" or "Se construyen las casas" - "Pasiva refleja" construction, more common than the previous one to say "the houses are built"
In "pasiva refleja" constructions the passive subject (the object if the sentence is made active) agrees with the verb (so it's "se construyen las casas" but "se construye la casa"). You have to remember that in this construction "las casas" or "la casa" becomes the subject (as in any passive sentence), even if it often comes after the verb. So in the sentence you give, "se va teniendo abundante información", the "abundante información" part is the subject and the verb agrees with it in number. If it was a plural phrase, such as "abundantes datos", then the verb should be in plural: "se VAN teniendo abundantes datos".
"Pasiva refleja" constructions are a bit tricky in Spanish, but they are very common, so you'll have to get used to them.