This is definitely the program you want. However yes there are some problems you may have, but they should all be able to be overcome easy enough. You may need to do some reading on the wiki. The problem is that the way a minecraft world is saved has changed over the years. McEdit is a versatile program, but we should do some preparation when working with very old worlds.
Basically you just need to get the worlds to load in the current version of minecraft.
Here are what the save formats are and when they were in use. Edit : Only certain version of the game contain converters from one save format to another.
Indev (McLevel) : c0.31 to a1.2.5
-I'm not sure if loading one of these worlds in a.1.2.6 will convert it or not.
Alpha (McLevel) : a1.2.6 to b1.2_02
-Load Alpha format worlds in b1.3 to convert to McRegion
McRegion : b1.3 to 1.1(12w06a)
-Load McRgion worlds in version 12w07a, 12w07b, or 1.2 to convert to McAnvil.
McAnvil (Extended Meta Data) : 1.2(12w07a) to 1.7.10(14w10c)
-Blocks could now have Extended Meta Data (Ex: Stone with a meta data of 15)
McAnvil (Meta Data and Blockstates) : 14w11a (1.8.8) to 15w34b and then 1.8.9
-Extended Block Meta Data blocks are still saved but no longer visible in game, they act as air blocks in game.
-Not many people knew how to use these in their builds, but I for one miss the extended meta data days.
McAnvil (Blockstates) : 15w34c (1.9) forward
-Block Meta Data no longer saved at all.
So by knowing when your world was last used we can start to convert them to the latest version. Here are the steps. Skip steps based on what format the world was saved in. Edit : You will have to load a world in a series of versions in the correct order to convert them until it is finally on the latest version.
1) Make copies of every world.
-Keep the originals safe.
-Only work on copies of very old worlds.
2) Get your Alpha save format to load up in McRegion format
-Load up each Alpha world in b1.3 and they will be converted.
3) Get your McRegion format Worlds to open into McAnvil format
Edit Correction : -Load up each McRegion world in 12w07a, 12w07b, or 1.2 and they will be converted.
5) Get your McAnvil format Worlds to open in the most recent version of minecraft
-because of the change from Meta Data to Blockstates you should load the world in the most recent version of minecraft
After all that each of your worlds should be playable in the current version of minecraft and McEdit will be able to completely read them. Always use the most recent version of McEdit found at https://khroki.github.io/MCEdit-Unified/
From there its all normal McEdit stuff.
Some problems you may have from very old worlds
1) Leaves on trees being wrong type for tree.- Alpha and some Beta Versions used a different layout for leaves meta data.
2) Doors facing wrong Directions -Doors got updated some time in Beta and use a new meta layout.
3) New spawned chunks in the old worlds wont look right next to the old chunks. -all old versions will come with this problem. Some more noticeable then others.
Edits are marked in Orange Text.