There may be times when mail messages will appear in Mail but will not have any content. When this happens the whole message may appear to be blank, or there may only be a few of the message's fields being used, so you only get a subject, or a sender.
The first thing that comes to mind when a message is received like this is that it is spam, and is just not being handled by the junk mail filter either on your mail provider's servers or on your system. If this is the case then you can set up a rule to handle these files, so it will remove files that do not contain a subject, sender, or other field.
Beyond the possibility of spam, there could be some issues with how Mail is displaying messages. Try toggling through different message view options, which are available in the View → Message menu.
Along with the view options, if there is a problem with fonts on your system, then Mail may be experiencing conflicts that prevent the message from being displayed. Check your installed fonts by running a Font Verification routine on them with Font Book (select all fonts, and choose "Validate Fonts" from the File menu). If there are any errors, then correct them and try running Mail again. Additionally, you can try changing the fonts that Mail uses for default views, the options for which are available in Mail's "Fonts & Colors" preferences.
If you suspect the message contains data and is not just spam, try creating a local mailbox on your system and copying the file to it. This will ensure the message file is local and not being synchronized or otherwise influenced by the mail server. With the message in the new location, try viewing it.
You can also try rebuilding the mailboxes that contain these messages. When you do this, it is likely faulty messages will disappear, so expect the blank ones to go away; however, if they do not then delete them and wait for new messages to arrive from the server.
Check with your e-mail provider to see if there are any server-side settings or message processing routines that could be affecting incoming messages. Sometimes mail servers will be paired with other services such as calendars and online discs, and an incorrect account setup on the server could result in odd behaviors with your e-mail client.
Lastly, try removing Mail's preference file, which is named "com.apple.Mail.plist" and is located in the /username/Library/Preferences/ folder. After doing this, you will need to re-enter your account information, but your previously downloaded messages and mailbox organization should be intact. This may help how Mail is interacting with the server and correct some issues that could be causing the blank message problem.