SQL procedure with cursor to check if values in table 1 are also in table 2
Doing that (checking if values in Table1 are or aren't in Table2) is typically done with a LEFT JOIN. Or a RIGHT JOIN if you want to get creative. Using a CURSOR in T-SQL should be you last resort!
Something like this:
SELECT t1.[columns]
FROM [table1] t1
LEFT JOIN [table2] t2 ON t1.[key] = t2.[key]
WHERE t2.[key] IS NULL


Style
There are a number of accepted standards for writing T-SQL. Some people write the keywords in ALLCAPS, others write them in lowercase - which convention you chose is entirely up to you and, in the end, doesn't matter.
What does matter though, is consistency.

and DateAdd(day, ZaN_DataRealizacji,CONVERT(DATETIME,'1800-12-28',120)) &gt;= @dzisiaj
AND DateAdd(day, ZaN_DataRealizacji,CONVERT(DATETIME,'1800-12-28',120)) &lt;  @jutro


and

select * from #Temp_Table
order by seria


shouldn't be in the same script. Pick a convention, stick to it, and thank yourself later :)
One helpful convention I've adopted, is comma-first. This:

SELECT ZaN_MagNumer,Zan_ZamSeria,Zan_DataRealizacji 


Would look like that:
SELECT 
     ZaN_MagNumer
    ,Zan_ZamSeria
    ,Zan_DataRealizacji 

This allows you to easily comment-out, remove, add or reorder columns while reducing the room for error.