I played the game and I only found one bug. When you go up the stairs and try to return back down, your character is invisible and you auto-lose.
Anyway, a few things that broke the immersion for me. The pixels of the text in the beginning look smaller than the pixels in the actual game. The text itself goes outside the box it is displayed it. This could have been better as a box that appears on the bottom and scrolls on key presses. It should use a bitmap font so that the pixels appear even.
The character and enemies appear to be able to move on the subpixel level. On the original Nokia, there are no subpixels. You need to round the positions of everything to be integers.
The enemies rotation uses sprite rotation, which again uses subpixels. The original Nokia 3310 did not support such sprite rotation. To achieve this effect, you would have had to draw the enemy facing each angle of rotation. Or at least 9 directions.
Otherwise, a nice game idea. With a bit more polish and the suggestions above, this game would be a solid entry for the jam.