If you are having trouble updating the Linux Mint repositories (packages.linuxmint.com) in the Update Manager, you are recommended to switch to another download server (a so-called "mirror"). Whether your problem is that the Linux Mint repositories are slow to update, or fail to update ("Unable to connect to packages.linuxmint.com:http:"), in both cases switching to a download server that is geographically more close to you will most likely solve your problem.
If you are having trouble updating the GetDeb repositories (archive.getdeb.net), that is a different problem. Please see here: viewtopic.php?f=47&t=118999. If you are having trouble updating other repositories, please make a new topic for that.
(For LMDE you have the mint-debian-mirrors to do this, see here: viewtopic.php?f=185&t=112047.)
Switching to another server is easy. The steps described below, including screenshots (it will look slightly different if you are using Linux Mint KDE). You can click the screenshots to zoom in, if needed.
- Open the Software Sources program from the menu. If you are using Linux Mint KDE you will be asked to authenticate by providing your password. Other editions of Linux Mint do this in step 6, so you will not be asked to authenticate here.
- On the "LinuxMint Software" tab, select "Other..." in the "Download from" selection box.
- In the window that opens, click the "Select Best Server" button.
- It will show the progress of testing all the download servers. Wait till this is done.
- Once it is done testing all the download servers, it will have selected and highlighted a suggested best one for you. To proceed, click the "Choose Server" button. (If you so desire, you may yourself browse and select another download server first. For example one in your country.)
- You will be asked to authenticate by providing your password (unless you are using Linux Mint KDE, in which case you already did this in step 1).
- After you have authenticated yourself, the download server will be enabled and shown in the "Download from" selection box. Updating the Linux Mint repositories should now be fast and failure free. You can close the window now.