Boeing's Dreamliners have been hit several times by small bugs, like fires in the batteries or other engineering issues. Are such incidents frequent when new types are introduced, and how much has the situation improved one year later?
You can get a rough idea by searching B788¹ on AvHerald.
Airlines do report technical problems² to their overseeing aviation safety board (in India it is, somewhat unusually, part of the civil aviation authority, DGCA; in most countries it is a separate agency, e.g. NTSB in USA). And those publish them.
Also for technical problems, aviation safety board of country of manufacture would be consulted, so NTSB should know about most technical problems of B787 and it should be possible to find them in their bulletins.
The Aviation Herald collects such reports from various sources. Only incidents that occur in flight get reported and only “interesting” subset of them, but if there were any serious problems with a type, they would come up.
Further if some problem requires mitigation steps to be taken, the civil aviation authorities publish airworthiness directives, that describe steps airlines must take (and under which conditions and until when) to be permitted to operate the aircraft. Since Boeing is based in USA, any airworthiness directive regarding it would most likely be first published by FAA and usually taken over by aviation authorities in other countries.
As far as I know, the batteries were the only serious issue of B787 that required immediate modification throughout the fleet. There are many small ones, like any aircraft, but there does not seem to be anything else that would be significantly more common or serious than on other types.
¹ AvHerald lists aircraft by their ICAO identifiers in the article titles (and full name in the text). The ICAO identifiers distinguish the series, so Boeing 787-8 gets B788.
² Those that affect safety. So non-working in-flight entertainment would not have to be reported, but a short-circuit in it should be.