First prints with my I3 X

[dav76]

Hi all,
I received an I3 X as a gift at the end of 2016, but due to logistical reasons, I only recently finished assembling it.
I took the chance to do some upgrades while I finished.
- I installed T8x2 lead screws, for now with simple nuts.
- I filed the plastic pieces to allow the lead screws to rotate more freely
- I opted for a steel 0.3 nozzle instead of the .35 brass that came with the hot end.

Yesterday I managed to get my first print out: an X, Y, Z calibration cube.
Not too bad but not good enough. I am posting some pictures as I would like to know what you guys can suggest as the causes of the issues with my print.
The X and Y were covered in a web of strings, which I removed. I do not know if these were support material or oozing. Any idea on how to check this?

Pictures and gcode are available here.

Thank you all in advance!