it does make a different. mydomainname.nl will rank good in netherlands but bad or not at all anywhere else. In google webmaster tools you can set geographic target for your site. If you have a country specific domain it will already be associated with that country/region and you can't change it. If you use .com or .net you can change it to a country or region if you want to target that area.
If your site is only for the Netherlands you can use mydomainname.nl but if your visitors are from all around the world it's better to use one of the global extensions.
From experience, I've done a lot of SEO for a keyword.net site, and the owner of the .com still outranks me most of the time (I beat her sometimes). I know for a fact she doesn't do any SEO because she got my whois information and called me and she told me she was a complete noob (and she was). So I came to the conclusion that the extension doesn't matter, but Google DOES favor .com over anything else. But not .net over .org, or .org over .info (again, from other experiences).
It doesn't matter ( At least it didn't use to ) but now since Google has started localizing its searches country wise you might get a better chance with a ccTLD because they seems giving a high priority for them in local searches.
Never heard something like that before, I think it might be about your domain name rather than it's extension.