MX record never points to an IP, "static" or "dynamic". Period. It points to some domain name which is the name of the server who should process the incoming mail for a domain in question.
Nobody cares how the records actually appear on the DNS server. You may create MX records and all records it references via RFC2136 dynamic update, by editing a zone file or by other manipulation with the backend database the DNS server uses, whatever. It's all up to you. The result will be the same: if the user requests MX record via DNS and it is being replied with valid information, it will work.
What is "static" or "dynamic" IP? The primary difference from your point of view is how often your machine receives IP address other than it has before. Others account for how often the user is changed behind that IP address. If it is "often", the IP is said to be "dynamic".
It is possible to set up a mail server answering on "dynamic" IP address, you have to maintain some A record with low TTL value to always point to currently used IP address (as I said before, it is irrelevant exactly how you achieve this). Then you may set the MX record to reference that "dynamic" A record. Your server residing on the "dynamic" IP will receive the mail for a domain.
The problem is that sending mail from that server will be greatly obstructed. Those are other servers who usually don't accept mail from IP addresses which they know are "dynamic" (where the user is frequently changing), because it is hard to determine who is responsible for this or that message.
The IP ranges that ISPs worldwide use for their "dynamic" clients are simply all listed in special "policy" blacklists (this is Spamhaus, there are other projects doing essentially the same). Usually mail from addresses that appear in those blacklists is either completely rejected or at least its "spam score" is set to very high value, diverting it to "greylisting" path or to eventual drop. You don't control other mail servers behaviour and therefore can't do anything with this. And there is completely no point in fighting this situation; just send your mail from IP address which Internet behaviour you carefully control, which is impossible to do if your IP address frequently changes.
Notice, you don't need to originate mail from the same system or IP address you receive mail; just remember the incoming server (who is listed in the MX record) sometimes need to originate some protocol-related messages too (delivery notifications), so it may need to use smarthost if it can't send mail directly. For instance, your ISP may provide you some SMTP relay which your mail server residing on a "dynamic" IP address may use as a smarthost, as Spamhaus suggests. Some ISPs actually block you from sending a mail directly and require the use of their relay for that purpose (this is what the comment by @Bob up there is about).
