I'm learning piano since December from last year (self-taught), so I'm a early beginner.
I find that the most difficult parts are:
1 - Paying attention at hand posture while playing (I often curve the hands instead of playing more at the front). I'm making this my main concern, because I don't have a teacher to help me correct it
2 - Sight-Reading. I was a violinist before learning the piano, so I can perfectly sight-read them separately. However, I haven't yet "triggered" my ability to read the two at the same time, at a satisfying speed. This actually helped to improve my memorization skills, because it's the only way I can play a piece...
3 - Not looking at the keyboard. I am improving this, so I can focus on sight-reading the score, but still, when the hand needs to change octaves and to do uncommon chord combinations, I still need to look...
4 - Coordinating hands. This took me a hard time on the very beginning, but I found that the note dropping technique by bernhard can work out wonders, specially at beginner easy pieces
5 - Playing piano/pianissimo with the left hand. I played a simplified version of a Chopin Prelude (Op.28 no. 7, from John Thompson Grade 2) and found that I couldn't play softly with the left hand and the pedal working. After lots of practice I can now play it very softly, but sometimes notes fail or are too loud...
Well, I think that's all for now...