The invites in MtG:DotP don't always pop up for your friends like they're supposed to. However, your friends can still join your game: In the steam friend's list, they need to click the arrow next to your name, then click "join game." They can bring up the friend's list ingame by hitting shift + tab, or simply by minimizing the game (alt + tab) and opening it from Steam.
You can do the same thing to manually invite friends using your friend's list.
Note that joining and inviting to games both work for most multiplayer Steam games, not just Magic the Gathering.
Some ways to fix Steam
Rebuild your ClientRegistry.blob
This is pulled off the Steam KB
Completely exit from the Steam client.
Go to C:\Program Files\Steam (or the Steam directory that was specified during installation).
Locate ClientRegistry.blob and rename this file to ClientRegistryOld.blob.
Restart Steam to allow the file to be recreated.
Test the issue once more.
Watch out for other programs!
It is known that programs such as Airfoil and F-Secure may cause problems with steam. Valve lists many of them here. Try toggling your virus protection, firewall, etc. to see what is causing steam to be unhappy. Try starting your computer in safe mode by pushing f8 before the windows logo comes up.
Try out the Steam Fix Program
This program claims to fix a wide variety of issues. Simply run it and follow the directions. The downloads are on various KB articles such as this one.
Validate game cache
If a game is having problems, rather than mess around with installs, try validating your cache! Cache validation is accomplished by right clicking the game in library and clicking the Local Files tab on top. Now, click the button that says Verify integrity of game cache. Be patient as this takes a long time
If all of this fails...
First, try a restart of your computer. Give steam another shot and if it doesn't work, it's time to reinstall. In this steam KB, it is outlined how to do a complete reinstall. ALL OF YOUR STEAM FILES WILL BE GONE. Please, make sure you know your password and you are willing to wait for games to re-download. If you want, move your steamapps ( C:\Program Files\Steam or C:\Program Files(x86) )
- Make sure steam is closed
- Open Control Panel
- Select Add or Remove Programs
- Scroll down to Steam
- Double click Steam
- Use the automated uninstall process
FOR ADVANCED USERS:
If you really want to wipe out your old install, head over to your Program Files or Program Files(x86) folder. Find the Steam directory and delete it. And, with regedit:
For 32-bit operating systems:
In the left-hand column of your registry editor, navigate to: HKEY_LOCAL_MACHINE\SOFTWARE\Valve\.
Right-click on Valve and select Delete.
For 64-bit operating systems:
In the left-hand column of your registry editor, navigate to: HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Valve\.
Right-click on Valve and select Delete.
In the left-hand column of your registry editor, navigate to: HKEY_CURRENT_USER\Software\Valve\Steam.
Right-click on Valve select Delete.
Don't do this if you don't know what you are doing, and please, make backups.
Best Answer
Friendslist of people are limited and only goes up by leveling up. That person has it filled, so you can't add him/her unless s/he levels up or unfriends someone.