In chess puzzles, castling is always possible. There is no need to specify that.
Puzzles and displaying castling rights, en passant, etc

It is true that in a real game castling event is specified, but this is a puzzle and in a puzzle I think we must always consider all possibilities when solving it.

The convention of chess problems is that castling is allowed and en passant is not allowed unless otherwise specified.
Suppose that the puzzle is changed to this:
And it is also stipulated that the position is legal (important, otherwise castling is still assumed to be legal!), then one can prove that the last move must be a king move or a rook move, and hence castling is not allowed, and hence the mate in two solution (1. Qa1 followed by 2. Qa8# or 2. Qxh8#) is valid as Black has no defense by castling.
I'm basing off Wikipedia, but I'm pretty sure composers of chess problems say the same.

Apparently, chess.com has taken the "chess problem or composition" convention with regard to castling, as opposed to the "practical tactics puzzle" convention. The former convention, used by chess problemists or composers, is that castling is assumed to be allowed, unless it can be proved by retrograde analysis that it is not possible. The latter puzzle convention is that castling rights are stipulated explicitly in the position given.
The world of chess compositions is distinct from practical OTB play. It has its own goals, motivations, aesthetics, and logic, and these do not always align with OTB considerations. I think it's fair to say that the vast majority of people are here to solve practical chess puzzles, not problems or compositions.
It should be noted, as we have seen today, that the correct solution of a puzzle can depend upon castling rights. This is why some other competitor sites always indicate explicitly the castling rights of each side, because they know their users are interested in tactical instruction. This is why I have brought this issue to the attention of chess.com staff, that they should include castling rights explicitly in the presentation of puzzles on the tactics trainer. I have never heard any response or acknowledgement from them.
Note that a similar comment can be made regarding pre-moves. At some other competitor sites, the explicit pre-move is always given. This removes any ambiguity regarding en passent.
Since the vast majority of people at this site are interested in puzzles, not problems, if someone (including the site itself) is posting a puzzle intending it to be interpreted as problem, then that should be stated explicitly, so that we all know we are solving a problem, not a puzzle.

Oh, that's where the confusion lies. I never knew anything like "chess tactics puzzle" before this, hence why I treat the puzzles as problems (and so I was quite dejected by the non-elegance of most puzzles in the forum, with plenty of useless pieces around).
In that case, yeah, I agree with the suggestion of specifying when the puzzles are intended to be compositions. This way, someone that's used with puzzles will not assume castling is not allowed like this, and similarly someone used to compositions will not wonder about how to achieve a mate in a complicated position while the target is only to win material (which tactics puzzle sometimes do).
In today's daily puzzle http://www.chess.com/forum/view/daily-puzzles/1172014---precise-mating-pattern it shows:
Which uses the FEN "4k2r/1pp4p/1p2K3/8/8/8/8/4Q3 w k - 0 1", clearing showing black's king-side castling rights. But when doing the puzzle, with the current interface, you are unable to see or grab the position's FEN, to know whether the position has castling rights or not, without first solving the puzzle or giving up. When doing the puzzle, I thought there was no castling rights because it wasn't specified. So a mate in 2 is possible by Qa1 followed by either Qxh8# or Qa8# depending on black's move. Can a link to the starting position's FEN be added to puzzles, without first giving up on the puzzle, so we can clarify things such as castling right and en passant without having to grab the full PGN with the solution?