I'd say there are some similarities to Liverpool last season. By January they still hadn't managed to win against a team in the top 10 and their record was scored 9, conceded 19 against them. He was getting criticised from all quarters for what he said in his interviews and for coming across as smug. The signings of Sturridge and Coutinho really injected a bit of life into them from January onwards and they carried on that form and confidence into next season. They still struggled against the top sides - in fact I don't believe they won a game against the top four last season and they obviously went out against Zenit in the EL - but they won the smaller games and picked up a fair bit of momentum.
We're in a similar position. Our record against the top six this year is poor (played 5, lost 4, drawn 1, scored 2 and conceded 11) but we are doing well against the rest (9 games, 7 wins, 1 draw, 1 loss, scored 22, conceded 4). Mata has obviously added an injection of quality into the team and he has brought the best out of Kagawa, similar to the effect that Sturridge and Coutinho had this time last year. Rodgers' Liverpool are an obvious example of how the results in a managers' first six months can be misleading and how it is possible for a team to turn it around completely.
People are talking about whether Moyes has stumbled upon the right system at United thanks to injuries but I believe something similar happened with Rodgers. Liverpool fans have happily admitted that he was stubborn and stuck to a rigid system at the beginning and that hindered them but then a quality player like Sturridge came in and forced him to find a way of accommodating him. He went through a phase of trying a 352 before ending up with that 4312 so it's not like he had a clear idea of how to get the best out of his best players right from the start, there was some experimentation and a "getting to know his players" phase. It took a while for him to get the best out of Gerrard too. In fact most Liverpool fans were saying it's time for him to be phased out and he is becoming a problem which is similar to what some of our fans are saying about van Persie.
People will obviously say that Rodgers and Moyes are completely different and Rodgers showed signs of progress and United are in a completely different position etc., but just to remind people what was being said about Rodgers last year. "He's out of his depth", "he's a mediocre manager", "Swansea have went up a level without him"...it's all the same stuff we've heard about Moyes.
I thought this was funny considering Revan's stance throughout this Moyes thread as well...