SMTP Diagnostics : Inbound Email

Compared to outbound email diagnostics, diagnostics of inbound email is quite difficult. Until the message is delivered to your server there is very little that you can do. It is rather like waiting for the post or a courier to arrive.

If someone reports problems sending you email, then your first question should be to ask if they have received a Non Delivery Report (NDR). This can give a reason for the failure. If they haven't received an NDR, then your next move is very much dependant on whether they have their own server or not.

If the sender has their own server (Exchange for example) then ask them to check their logs to see what server the email message was delivered to, if the message was delivered at all.

If the sender does not run their own server, or the message was sent by their server to an ISPs server then your options are almost none as you will have to wait for the ISP server to deliver the message. If it is the sender's ISP then they could call them up and see if there is a problem, but most ISPs are not interested in email issues of a small customer or will simply say there is nothing wrong with their network.
If the message was delivered to your ISP and you start getting regular failures or delays to messages through their server then you should look at switching to direct SMTP delivery.

If the message was delivered to your server, then you need to track what happened.

Message tracking (Exchange 2003 - Exchange 2007) can help with this, as it will show what Exchange did with the message. 
SMTP logs on Exchange 2003 and Protcol Logs on Exchange 2007 and higher, can also show the connection, but their detail is very basic and will not show much more information of use.

If the message tracking logs show that the message got to the categorizer and stopped there, then that is usually an indication that Antivirus or Antispam software has blocked the message. You need to look at the quarantine.
If the Microsoft Exchange Intelligent Message Filter (IMF) (Exchange 2003 only) has blocked the message then this will be clearly shown in the tracking logs.

Obviously if you are using anti spam products that use blacklists, you will have checked those first and white listed as appropriate.