Conversion failed when converting the varchar value 'simple, ' to data type int

In order to avoid such error you could use CASE + ISNUMERIC to handle scenarios when you cannot convert to int.
Change

CONVERT(INT, CONVERT(VARCHAR(12), a.value))

To

CONVERT(INT,        CASE        WHEN IsNumeric(CONVERT(VARCHAR(12), a.value)) = 1 THEN CONVERT(VARCHAR(12),a.value)        ELSE 0 END) 

Basically this is saying if you cannot convert me to int assign value of 0 (in my example)

Alternatively you can look at this article about creating a custom function that will check if a.value is number: http://www.tek-tips.com/faqs.cfm?fid=6423

If you are converting a varchar to int make sure you do not have decimal places.

For example, if you are converting a varchar field with value (12345.0) to an integer then you get this conversion error. In my case I had all my fields with .0 as ending so I used the following statement to globally fix the problem.

CONVERT(int, replace(FIELD_NAME,'.0',''))

Given that you're only converting to ints to then perform a comparison, I'd just switch the table definition around to using varchar also:

Create table #myTempTable(num varchar(12))insert into #myTempTable (num) values (1),(2),(3),(4),(5)

and remove all of the attempted CONVERTs from the rest of the query.

 SELECT a.name, a.value AS value, COUNT(*) AS pocet    FROM  (SELECT item.name, value.value   FROM mdl_feedback AS feedback   INNER JOIN mdl_feedback_item AS item        ON feedback.id = item.feedback  INNER JOIN mdl_feedback_value AS value        ON item.id = value.item    WHERE item.typ = 'multichoicerated' AND item.feedback IN (43) ) AS a  INNER JOIN #myTempTable      on a.value = #myTempTable.num GROUP BY a.name, a.value ORDER BY a.name