What is displayed next to a cell in which a formula error occurs?

The # will always be the first character shown and it will be followed by the name of the particular error. Common ones could be:

#REF!

#VALUE!

#NUM!

If you see the # repeated, it indicates that the cell is not wide enough to show the value in the cell. It is not necessarily an error.

OR

A green triangle in the upper left corner of the cell