Cleaning up ID conflicts is tedious, but not hard.
First, you clean up the block conflicts - those are the ones that crash the game or lead to startup errors. They are easy because everytime it happens, you get an error log that tells you exactly what went wrong where.
However, a select few block IDs and pretty much all item IDs conflict silently, so you need to manually look for them. Here's how:
Go into NEI's options ingame and create a dump of all used "Blocks/Items" IDs.
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https://www.dropbox.com/s/amqejji5oddzz08/2013-12-03_18.56.30.png?dl=0
You will get a .csv file that you must open with a spreadsheet program like Excel or competing products.
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https://www.dropbox.com/s/wft3jx8pg3emux9/idconflict1.png?dl=0
Split the raw csv data into 5 columns - each program has its own way to do that automatically, ask Google for help if necessary. Also expand the columns so that you can read all the contents.
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https://www.dropbox.com/s/ke047rz4vsrkwd7/idconflict2.png?dl=0
Then, go line by line through all the IDs. You want to make sure that the three last columns all show matching information. For example, I have marked a line green here in the screenshot.
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https://www.dropbox.com/s/x6i0e2mnt91cj0m/idconflict3.png?dl=0
As we can see, the item 22411 claims to be from the mod Thaumic Tinkerer. It's name is given as "item.ttinker:spellcloth", so this seems to match up. Finally, the class the code for this item is saved in is called "vazkii.tinkerer.common.item.ItemSpellcloth". This, too, matches the information in the other columns. Clearly everything is in order here, there is no conflict over ID 22411.
On the other hand, here we have a classic ID conflict:
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https://www.dropbox.com/s/qoty5p17hag9gav/idconflict4.png?dl=0
IDs 4089 through 4093 all claim to be taken up by the Greg's Lighting mod. However, in the following columns we see block names and class names from Biomes O'Plenty! Here, one mod overwrote something the other mod claimed first, and this will cause you grief ingame even if it doesn't throw any startup errors.
Just be on the lookout for cross-mod API calls. When Railcraft adds its backpacks, for example, it derives them from a Forestry class. This is normal and intended.
Thankfully, NEI can not only dump you used IDs, but also free IDs (or even both at the same time). That way it is easy to see where you can move conflicting items to. Just be careful to differentiate between
blocks (anything from 0 to 4095) and
items (anything from 4096 to the cap, something like 32,000+). If you mix these up, you'll get bad errors.