Is that you can't be sure you're actually reading something that is 100% equivalent to the original. For some examples, consider the Essential Spiderman, Volume 1:
Supergirl's first encounter with the Legion of Superheroes, where they explained that they were the children of the original Legion members. However, later on it was decided to put Supergirl in the same Legion as Superboy, and so when that story was reprinted the text in several panels had to be completely changed.
Another, very early example comes from Batman Annual #3. As I discussed a long time ago, the origin of the second Two Face initially involved a romantic triangle between the actor Paul Sloane, a prop man and the latter's girlfriend. Apparently in 1963 the Comics Code Authority decided that the reference to Sloane stealing the prop man's girlfriend had to go, and so a couple panels were redrawn and several others were deleted in their entirety. Update: A reader named Christopher pointed out in an email that in all probability the real reason for the change was the violence inherent in the prop man using acid to burn Sloane's face. I find this argument convincing, particularly because a splash panel in another story from Batman Annual #3 was also changed. Here's how it appeared:
Sometimes reprints are amended for cultural reasons. ASM #17 had the web-slinger mocking the Green Goblin's throwing arm:
When that comic was reprinted in England years later, the insult was changed to say that the Gobby would never make it as a "fast bowler" (the equivalent of a pitcher in the sport of cricket).
Another example involves the Famous First Editions. In the mid-1970s, DC reprinted oversized copies of some of their earlier and more valuable comics, including Action #1. The comics came with an outer cover identifying them as reprints, but underneath was purportedly a complete facsimile of the original, ads and all.
Well, almost. Here's the cover of Action #1 as it appeared inside the FFE:
1. There is no white glare on the front fender in the FFE.
2. The man in the foreground is dripping sweat in the original.
3. There are two loose rocks by the front of the car in the original.
4. The running board is yellow in the original, green in the FFE.
There are a couple more problems with reprints that I can think of offhand. Sometimes the space allotted for the reprint doesn't match the size of the original, and so some parts are excised. For example, when ASM #122 first came out, it included this page:
If I recall correctly, DC also deleted sequences from the reprinted second part of a two-part story that had originally served to recap the previous issue, since those scenes were now superfluous.
DC also changed the artwork on the story about the deaths of Jonathan and Martha Kent. As I discussed a couple years back, DC had printed the story in 1964 or so, with the Kents as oldsters. But in Superboy #145, the Kents were suddenly transformed by an alien TV producer, appearing now as a couple of thirty-somethings. Thus, when the story of their passing was reprinted, their faces had to be redrawn to make them younger.
Overall, while reprints are often a cheap way to fill in the blanks of your knowledge of a character, always be aware that what you are reading may not be completely what appeared in the original.
Any other examples of reprint problems? I know, for example, that sometimes DC had their artists trace over old stories in order to reprint them; the Alfred origin in Batman #216 is an example of this.
Update: David's Amazing Adventures points out a coloring change in a reprint of the Thor origin story.
Update II: Scott Edelman notices a change in Spiderman's origin that took place between Amazing Fantasy #15 and ASM #1. BTW, I think the next time Spidey's origin was retold was in ASM Annual #1, and they went back to the Amazing Fantasy version.