GROUP BY + CASE statement

Your query would work already - except that you are running into naming conflicts or just confusing the output column (the CASE expression) with source column result, which has different content.

...
GROUP BY model.name, attempt.type, attempt.result
...

You need to GROUP BY your CASE expression instead of your source column:

...
GROUP BY model.name, attempt.type
       , CASE WHEN attempt.result = 0 THEN 0 ELSE 1 END
...

Or provide a column alias that's different from any column name in the FROM list - or else that column takes precedence:

SELECT ...
     , CASE WHEN attempt.result = 0 THEN 0 ELSE 1 END AS result1
...
GROUP BY model.name, attempt.type, result1
...

The SQL standard is rather peculiar in this respect. Quoting the manual here:

An output column's name can be used to refer to the column's value in ORDER BY and GROUP BY clauses, but not in the WHERE or HAVING clauses; there you must write out the expression instead.

And:

If an ORDER BY expression is a simple name that matches both an output column name and an input column name, ORDER BY will interpret it as the output column name. This is the opposite of the choice that GROUP BY will make in the same situation. This inconsistency is made to be compatible with the SQL standard.

Bold emphasis mine.

These conflicts can be avoided by using positional references (ordinal numbers) in GROUP BY and ORDER BY, referencing items in the SELECT list from left to right. See solution below.
The drawback is, that this may be harder to read and vulnerable to edits in the SELECT list (one might forget to adapt positional references accordingly).

But you do not have to add the column day to the GROUP BY clause, as long as it holds a constant value (CURRENT_DATE-1).

Rewritten and simplified with proper JOIN syntax and positional references it could look like this:

SELECT m.name
     , a.type
     , CASE WHEN a.result = 0 THEN 0 ELSE 1 END AS result
     , CURRENT_DATE - 1 AS day
     , count(*) AS ct
FROM   attempt    a
JOIN   prod_hw_id p USING (hard_id)
JOIN   model      m USING (model_id)
WHERE  ts >= '2013-11-06 00:00:00'  
AND    ts <  '2013-11-07 00:00:00'
GROUP  BY 1,2,3
ORDER  BY 1,2,3;

Also note that I am avoiding the column name time. That's a reserved word and should never be used as identifier. Besides, your "time" obviously is a timestamp or date, so that is rather misleading.

can you please try this: replace the case statement with the below one

Sum(CASE WHEN attempt.result = 0 THEN 0 ELSE 1 END) as Count,

Aliases can be used only if they were introduced in the preceding step. So aliases in the SELECT clause can be used in the ORDER BY but not the GROUP BY clause.

Reference: Microsoft T-SQL Documentation for further reading.

FROM
ON
JOIN
WHERE
GROUP BY
WITH CUBE or WITH ROLLUP
HAVING
SELECT
DISTINCT
ORDER BY
TOP

Hope this helps.