Wow! I'm having the worst time with my dryer. When I first moved into my house I blew a fuse about a week after living here so I replaced it... that was about 6 months ago. Then about 2 weeks ago I blew another fuse so I replaced it again and I have blown about 3 sets of fuses in a week. I'm not quite sure what a blown 30 amp fuse is supposed to look like but it like crumbles to pieces dang near and smells like its burning. Some of the plastic is even melted where the fuse sits... any ideas?. you can kind of see the discoloration behind the fuse where it has started to melt

Yep, sure are having problems. The fuse holder probably needs to be replaced and there are some places on the net that specialize in antique boxes.

Note that the plating has worn off and the resistance is high, so it gets hot and deteriorates.

Get yourself some 400-600 grit sandpaper and lightly sand the bad fuse terminal to remove the corrosion. Generally, you don't want to remove the plating, but it looks like it's gone anyway.

Then get some dialectric grease such as this one: PERMATEX DIELECTRIC TUNE-UP GREASE, .33 OZ. TUBE (81150)

At a hardware or auto-parts store and coat the terminals and fuse ends with a light film before installing.

Your not done yet.

You have to check the inside of the fuse box to see if the wire to that fuse is loose and/or discolored. This may not be something your willing to do. If it's discolored it needs the same treatment.
It would not be a bad idea to check the other end for loose connections with the fuse block pulled, of course.

I won't suggest doing it live, but you can pull the main breaker and take the cover off and snap a picture. We can then point out areas that you need to avoid inside the box with the main pulled.

The advice by Kiss is valid, however, the damage done to the interior portions of the panel where the fuse holder plugs into I am sure is damaged beyond repair.

The insulating properties of the plastic inside has been lost, and will continue to decompose. Some day you will have sparks coming out of the panel, when you least expect it.

The panel needs to be replaced. Good time to consider upgrading from fuses to at least a 100 amp service with circuit breakers.

Wow! Thank you! If I called someone to come and fix this... is it a spendy fix?

PLEASE follow TK's advice here!