I read the manpage and the only time they use --dest-port or -dport is when they're using an extension.
I just wanted to do some basic filtering without extensions. I tried:
iptables -A INPUT -p all -dports 6000 -j DROP
and I got that 6000 was an invalid argument.
So I try different syntax using --dst-port and it saays that dst-port isn't correct syntax. I just have 3 or 4 ports to block for a short period of time. Am I doing something wrong?

-p all includes a wide number of protocols besides tcp and udp such as icmp, gre, etc (see /etc/protocols). Many of them don't have a concept of a 'port' like icmp for example. So you need to specify the tcp or udp protocol. Also use two dashes for the secondary options like -p tcp --dport 6000

That did the trick. What exactly is mangling in the sense of a firewall? What function does it serve?

The mangle table is used for modifying various parts of the packet. For incoming packets, it allows you to change these parameters before any routing decisions are made which is useful in certain situations. It's extrememly important not to do any filtering or NAT in this table as the rules will be ignored. In most situations you won't ever need to do any mangling, but if you wanted to change the TTL of an outgoing packet (to hide the fact that it's behind a NAT firewall) then you could modify the TTL in the mangle table. This is a really great HOWTO that can explain iptables pretty well, take a look:

http://iptables-tutorial.frozentux.n...-tutorial.html