What are the maximum number of recipients I can bcc on an email message in Outlook (or any other mail application)?
What happens if I exceed that limit?
Do I get any kind of error or warning message, or do some people just not get the message?
The maximum number of recipients in an email is 100 - that includes To, CC, and BCC all together. That's a standard limit, not one MIT chose arbitrarily. This limit is important for consistent performance as many mail systems outside of MIT will reject messages that contain more than 100 recipients.
While your email client may allow you to attempt to send a message to more than 100 recipients, it will not work. The limit is enforced by the MIT mail servers. You will receive a bounce message and none of your recipients will receive your message.
Using a Moira or Mailman list is the recommended best practice for sending messages to a large number of users at once. For more information, see Email Lists (Moira and Mailman)
For information on daily sending limits, see: Why am I getting a Bobo with your canned meat email error message?