Running your own DNS will not solve the blacklisting issue. Your mail server is blocked for legitimate reasons. The vast majority of spam originates from compromised hosts on dynamic addresses. Even if your ISP had not provided there dynamic IP ranges for blacklisting, you would still get caught by rDNS validation as the PTR record for your IP will not match your domain.
While you risk loosing email when your dynamic address changes, you can receive email on a dynamic addresses. I would recommend asking your ISP for a fixed address. Some ISPs provide them on request, other charge a fee. They should also be willing to set the PTR record on your static address to your mail servers DNS name.
The proper way to send email if you are on a dynamic range is to use your ISPs mail relay. Configure your email server to send all outgoing email to the relay for delivery. This should resolve your issue with being blacklisted.
If you configure SPF (highly recommended), then include your ISP's record, or list their relay server(s) in the SPF record for your domain.
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@JonasWielicki Dynamic IPs are typically blacklisted. I have a dynamic IP from my ISP, these ranges are by default blacklisted because of spam. Email servers work with other email servers that have good reputation which are determined by central services like Spamhaus. If your email server IP is on this list other servers won't accept your emails. – user3590149 – 2014-10-12T16:44:46.943
@JonasWielicki Took your advice for the DNSSEC question and post separtely http://superuser.com/questions/825225/dnssec-client-software
– user3590149 – 2014-10-12T16:53:53.573