After you have beaten the Elite 4, there is much more that can be done in Pokemon Diamond.
After beating the Elite 4, you can get the National Pokedex by having SEEN all 150 Pokemon in the Sinnoh Pokedex. After you have SEEN 149 of the 150 Pokemon in the Sinnoh Pokedex, you can go talk to the town elder in Celestic Town to get a tale about the other version's legendary Pokemon, Palkia from a book lying on the table. That will give you the final seen Pokemon in your Sinnoh Pokedex. After you have done that, you need to go talk to Professor Rowan, who will then be interrupted by Professor Oak. Professor Oak will then give you the National Pokedex.
After getting the National Pokedex, many new things will have opened up:
Fly to Eternea City and go to the Old Chateau. Outside the Old Chateau, the second Gym Leader will be waiting for you with a little side-quest. After talking with the second Gym Leader, walk inside the Old Chateau and go up to the second floor and walk into the first room on the left (the one with the television). You should find that the television is now turned on. Walk up to right in front of it and SAVE THE GAME. After you have done that, press the A Button and you will start a battle with Rotom! Be warned, he is at the massive level of Level 15 :). Make sure that you catch him, as there is only one of them in the game.
Fly to Veilstone City and walk south onto Route 214. Continue walking south until you see a new pathway that has opened up before reaching Lake Valor Waterfront. Walk down that pathway until you get to a cave in the side of the wall. You will need a Pokemon with Rock Climb, and maybe one with Rock Smash. Enter Turnback Cave and then keep on taking the same exit until you reach Giratina! Giratina is one of the new Legendary Pokemon that you can catch after obtaining the National Pokedex. SAVE right before you enter battle with him, and bring your strongest Pokemon, because Giratina is at Level 70! Make sure you catch him as there is only one in the whole game.
Fly to Pal Park and talk with Professor Oak, who is milling about outside to get the Poke Radar. The Poke Radar is a Key Item that, when used, gives you the potential of seeing many new kinds of Pokemon from the previous games. Such Pokemon include Larvitar, Nidoran M, Nidoran F, and others.
Speaking about Pal Park, if you have Pokemon Ruby/Pokemon Sapphire/Pokemon Emerald/Pokemon Fire Red/Pokemon Leaf Green inserted into your GBA Slot of your DS, you will have gained the ability to "migrate" Pokemon over from your Emerald/Ruby/Sapphire/Fire Red/Leaf Green versions onto your Pokemon Diamond version.
Another new feature that has been added is the fact that you can find some of the Pokemon from previous versions in the game when you have the Pokemon Sapphire/Pokemon Ruby/Pokemon Emerald/Pokemon Leaf Green/Pokemon Fire Red versions inserted into the GBA Slot. You will find them in Routes that you would never have found them before in.
Fly to Snowpoint City. Remember that Temple that you couldn't enter before? Now that you have the National Pokedex, Candice will give you permission to enter the Snowpoint Temple. Located at the bottom of the Snowpoint Temple is Regigigas, another one of the new Legendary Pokemon that can only be obtained after getting the National Pokedex.
While you are in Snowpoint City, talk to the Sailor who is standing on the pier to gain access to the Battle Zone. The Battle Zone is a huge island with 5 new routes and many strong Pokemon (all above level 50).
After you gain access to Battle Zone, you will also gain access to the Battle Tower, which is located in the Fight Area. On weekends, your rival will be standing outside of the Battle Tower, ready to fight you again :).
After you gain access to Battle Zone, you will gain access to Mt. Stark, which is a new area with a secret treasure inside. It also houses another of the new Legendary Pokemon whose name is Heatran. You can only obtain him after gaining the National Pokedex.
Fly to Canalave City. Speak with the sailor's family to find out that the sailor's son has gotten sick and needs the Lunar Wing. Talk with the sailor to gain access to Full Moon Island, where another of the new Legendary Pokemon that can only be obtained after getting the National Pokedex resides. Its name is Cresselia, and like Mesprit, after you talk to it, it will be roaming around Sinnoh.
Go back into Victory Road. Remember that guy that was blocking that offshoot from Victory Road? Well, now that you have the National Pokedex, you will have gained access to that offshoot now, which has a whole new route for you to explore. Route 224! What secrets does Route 224 hold?
If you have a completed Pokemon Ranger game, you will now be able to transfer over a Manaphy Egg from that game.
Source(s) http://answers.yahoo.com/question/index?qid=20080827031901AAkp6vg