File Attachments appear to cause far more difficulties in Thunderbird than they should. Part of this is the somewhat quirky way Thunderbird deals with attachments and part is due to most Quirks in Other email applications that send not quite standard email to Thunderbird.
The main causes of difficulties are the 'Helper Application not found' error message and winmail.dat files which are discussed below. as well as the newer problem of attachments simply not appearing at all.
This is another of those innovative ideas that Microsoft had that just didn't work out well for the average user. Microsft invented the winmail.dat file for use in corporate networks using Microsoft Exchange servers. Unfortunately, most of the use of Outlook that the average person sees is in Internet Mail. Internet mail is not a closed environment so proprietary solutions such as this just don't work. The result is you get this silly file attached to your mail, with no really simple way to either open it or view it.
There is an add on LookOut, which tries to do something useful with these files and display their content. But the only real solution is to contact the person sending you the mail and explaining to them that their mail client in not configured correctly and that they need to fix it so you can read the attachments they are sending you.
When telling someone their software is not configured correctly it can be a bit difficult, but if you give them this handy link to KB138053 on the Microsoft web site they should be able to fix things so they are not sending out mails that no one can read easily.
Helper Application not found
This is one of Thunderbird's Quirks. It actually stores a list of applications to associate with file types (based on the MIME information in the email). This works quite nicely most of the time, until a new version of one of these programs come out that moves the location it is installed in. Then this message rears it's head. Thankfully it is easy to cure.
On the Tools Menu, you will find options. In option there is a button called attachments, this is where all this file type association stuff is stored in Thunderbird. There is nothing needed to fix this problem other than to locate the association for the file type and delete it. Next time you ask Thunderbird to open a file of that type it will ask you what to do with the file and you get to select the correct application. You can also click the save and have Thunderbird remember exactly what to do with that file type.
Thunderbird tries to open the file with the wrong program
This is usually caused by the senders email program incorrectly identifying the attachment file type in the MIME encoding of the file. The simple answer for this, if you get mail from the same people that cause this problem all the time is to install the Open Attachment By Extension add-on. This add-on opens the file based on the extension in the mail, not the MIME type which is how Thunderbird normally selects the application to open an attachment
Attachments don't Appear.
Following the fixing of a bug in Thunderbird that caused you to be unable to detach an attachment from a mail, attachments generated by many email programs have stopped being displayed. The underlying cause is complex and the discussion I have seen on the topic indicates that it is 'non trivial to fix'. My experience with Thunderbird leaves me to translate that as 'it will be a long time before we fix this' to good news is that there is an add-on that allows the attachment to be displayed. Simply installing this add-on adds a new entry to the "message body as" on the view menu to allow all 'parts' of a message to be viewed. Because of the way it works, all sorts of parts of a message are displayed as an attachment, including digital signatures and images embedded in HTML messages. For more information on the problem and the issues, the meet the developer page from the add-on is full of background.