This problem occurs, when you have a column with a formula that sometimes returns an error.  That is very typical for all kind of look-up situations .  Let’s say, you have a column E with formula that returns good values and errors.  You need to count how many errors are in that column.

Enter formula

=SUM(IF(ISERROR(E2:E10),1))

and press Ctrl+Shift+Enter while still in editing mode.
You should see two things.  First, your formula turns into

{=SUM(IF(ISERROR(E2:E10),1))}

with square brackets around it, and second, you got you a correct cells with errors count.  This is it.

If you need to count cell without errors, you can use this formula:

=SUM(IF( NOT( ISERROR(E2:E10)),1 ))

and press Ctrl+Shift+Enter while in editing mode.

You can further experiment with this solution.
For example, try using:

=COUNTIF(E2:E10,"=#N/A")

I found that this formula works, if your errors happened to be of type #N/A .

Note: above method tested in Excel 2010, 2013 and Excel 365 [2017-06-15 TH]

In case you need to count non-blank cells in a range use this formula:

=COUNTA(E2:E10)

Formula above allow for multiple non-continuous ranges.

To go to the bottom of data and not to the bottom of the sheet, use  End and Home (not tested yet) instead of usual Ctrl + End