How could I create a macro that would check each cell of column A, find the words that are not in the defined dictionary, and write them (separated by space) in the next cell. In the picture below you can see an example of the worksheet after that macro was completed.

The complete idea was to get a (varchar) column from a database and use excel to spell check it. The next step would be to send an e-mail to the user in charge, containing the rows that contain at least one word in column B (along with the column id, of course). I think that I could do the rest of the work, except this step of getting the erroneous words. If you can think of another idea to spell check a db column, I would be grateful if you shared it with me. Thanks.
You can use VBA to call the built-in Office dictionary using Application.CheckSpelling
This is the syntax:
Function CheckSpelling(Word As String, [CustomDictionary], [IgnoreUppercase]) As Boolean
… and here is an example that meets your requirements: