There is one scenario for each case:
add 3 tags.
1) 1a:1a
2) 2a:2a
3) <empty>:3a

1) Host.

Error message - Invalid parameter "/1/tags/3/tag": cannot be empty. No sorting (empty tag stays on position - 3).

2) Items.

First time pressing Update button - Invalid parameter "/1/tags/3/tag": cannot be empty. The third tag changed its position and placed first. Clicking update one more time error message changed to the correct one - Invalid parameter "/1/tags/1/tag": cannot be empty.

3) Triggers.

Pressing update button - Invalid parameter "/1/tags/1/tag": cannot be empty. Tag with empty name moved to first position and correct error message displayed.

4) Templates.

Clicking first time Update button - Invalid parameter "/1/tags/3/tag": cannot be empty. Tag moved to the first position. After clicking update button one more time - still the same error.

So right now we have 4 different methods to display errors for incorrect tags.