Original User: erictrice
Bradley,
The default resampling in the Project Raster tool is Nearest. You can't use that otherwise you get the result you did. Here is the help for this parameter.
"The NEAREST and MAJORITY options are used for categorical data, such as a land-use classification. The NEAREST option is the default since it is the quickest and also because it will not change the cell values. Do not use NEAREST or MAJORITY for continuous data, such as elevation surfaces."
Go back to your original data and project it again using bilinear, then run the hillshade with z factor 1 (assuming X,Y,& Z all have same units). Do not change the cell size of the output hillshade.
You should also build pyramids with Bilinear, which can be set in the environment settings. If you resample with bilinear when projecting but build pyramids with nearest (the default) it could still look weird. Also, as mentioned above, set the display resampling to Bilinear for a better display.
Best,
Eric