Immigration Canada sent our (mine and my partner) all information, including addresses, bank statements, tax information, personal correspondences, employment information, literally every paper what had been collected in our file to the wrong address.
Could it be a reason to sue them? Could it be a subject of the Privacy Act?

Unusual for this to happen. Did you not notify them of a change of address? There has to be a very plausible reason for this happening.

If correct, there could be an inquiry, but unless you have a pretty good case and lots of evidence, and possibly a lot of money to hire a good lawyer, no chance.

In our application we initially specified our correspondent address. They left it out. The change of my partner's (who is my sponsor) address was not needed on the first place, because. The address for correspondence was already in our application.

Also just after the interview, we notified the Imm. Mississauga of a change of address officially.

Later, after they sent the documents to the wrong address, we got to a such struggle with them to get the documents to the right address. They literally wrote that they are "not obliged" to sent the documents to the address we request to ( even though that was the address for correspondence in our application).

Finally, we did a screen dump of the section in our application where we put his address for correspondence and sent them it as a proof. Only after, he got the documents from them. This delayed our appeal for 3 and half months.
And we met the nastiest attitude from them I have ever seen in my life from officials.

In some time he got a letter from Immigration where they explained reasons for accepting out appeal (bc. As I told we were late), they admitted their mistake and sent us provisions for the Appeal.

Then, guess what? A package with ALL our information, including bank statements, tax information, personal data, employment details, everything what was collected in our file and would be needed for the appeal, came AGAIN to the wrong address!

... They literally wrote that they are "not obliged" to sent the documents to the address we request ...

Wow, it's even worse than if they had figuratively wrote that. :)

Do you have any evidence that somebody else opened it?

Did you suffer any damages?

The evidence is an e-mail from our former landlady where she told me that a letter from imm. Came to the name of my sponsor even though he moved out a year ago (that is why we specified in our application his address for correspondence - on a case of his move, as it happened) and that she opened it.

She found me through a social network via internet, and let me know about this.

The damage we had was a delay with our appeal for 3 and half months and moral suffering we went through with immigration. We got from them such a vicious attitude when we pointed out their mistake they made on his address for correspondence.

We keep all correspondence with the immigration.

In the second time, when they AGAIN sent ALL our data ( see my postage above), she also opened it, when I warned her not to open, but just bring it to the post office with a note "moved out". Finally she did.

This time it was a delay for a month.