In order to use the Desktop Connector with a wiki that is using a self-signed SSL certificate, the .NET Framework has to trust the certificate. Here's how you can do this.

Here, you see a web site that has an untrusted certificate. Click "Continue to this webpage."

Click "Certificate Error", and then "View certificates" on the pop-up window.

On the Details tab of the Certificate window, click "Copy to file". You will see the Certifcate Export Wizard. Click Next, select DER encoded binary X.509 (CER) and click Next, and then enter in a filename to save to. Click Next then Finish, and you should be told "the export was successful".
Now, click Start, Run and type MMC.

The Microsoft Management Console opens. Click File, Add/Remove Snap-in. Click Add, select Certificates from the list, and click Add again. You will be prompted for which certificate store to manage - select "Computer account" here (the .NET framework does not see user certificates).

Now, you will see the console with the computer's certificate store. Expand "Trusted Root Certification Authorities", right-click Certificates, and select All Tasks/Import.

You are now in the Certificate Import Wizard. Click Next, and enter the file name of the certificate you exported in the first step. Click Next.
You should be prompted to place the certificate in the "Trusted Root Certification Authorities" store:

Click Next and Finish. You should now be told "the import was successful".
Now, if you refresh the Certificates window, you should find the certificate you just imported:

Congratulations - your .NET application should now trust the certification path to your wiki.