AlphaZero lost 6 games to Stockfish in a 1000-game match from the starting position, at least one of which was with the white pieces: A game A0 lost with white. For some reason, these games haven't received much media attention. Does this mean AlphaZero hasn't solved the game of chess yet? So, there is still scope for improvement? The media's report that AlphaZero is the perfect chess-playing machine is false.
AlphaZero hasn't solved chess, and it won't until it can find a strategy that results in the same outcome of the game given perfect play from both sides. According to Wikipedia:
A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.
Since AlphaZero has lost games to Stockfish with both colours, we can assure it didn't solve the game. AlphaZero plays itself in training games. Had it solved the game, all these AlphaZero vs AlphaZero games will end up in one same result: either a win for white, a win for black or a draw.
There is no such thing as perfect playing machine in chess. Google never claimed their engine was able to solve the game.
AlphaZero hasn't solved chess - to do so you'd need to know from the starting position which side wins (or if the game is a draw). This is in principle doable with a 32-piece tablebase, but in practice it's impossible.
“Yes,” replied God, “I have done the 32-piece endgame.”
“Ahh,” said Garry, “Of course that is trivially easy for you.”
“No, no,” said God, “it was really tough. More than 10^35 legal positions — it took the matter from a good-sized planet to store. But let us play. You can have white.”
10^35 is a fantastically large number. If it takes one byte to store one position, one gigabyte is still only 10^9 positions, 26 orders of magnitude off the required number. So no, AlphaZero has not solved chess, and there's no way to do so in the foreseeable future.
Naturally this means there is still scope for improvement. If AlphaZero were a conventional engine its developers would be looking at the openings which it lost to Stockfish, because those indicate that there's something Stockfish understands better than AlphaZero. AlphaZero is a neural network engine however, which makes how to improve it less obvious. I am not an expert on neural networks, but you can follow the development of Leela (which is a reproduction of AlphaZero, based on the paper) on its developer blog.