I think it's mainly devoted LSAT nerds that notice the changes. They're pretty subtle. I would say that Games changed the most and LR the least.
Games -
The big difference with older games is that there are more "wildcard" games ... i.e. within a Games section you might see one (or even two) games that don't really resemble anything you're used to doing. You'll still see a fairly ordinary Ordering game and a fairly ordinary Grouping game, but the other two might push your imagination/flexibility a little bit to improvise.
Modern game sections tend to have nothing but Ordering, Grouping, and Hybrids of the two. That doesn't necessarily make them easier, though. While the game types have gotten more standardized, the games themselves are often tricky versions of our standard types. I would say there's a bit of a trend away from powerful up-front deductions and more towards the laborious, "test-each-answer" type games.
Also, there is that new question type, which we call Rule Equivalency. You normally get one of those per section. The question says something like, "Which of the following rules, if substituted for [rule X], would have the same effect in determining the possibilities in the game?"
Yuck. As bad as that new question type is, though, you get ONE of them per game section. So just skip that one question and get the other 21 right.
READING COMP -
The big change is that starting around June 2007, one of the four RC passages is a short dual passage. Clearly, these play out a little differently from a normal passage, but not radically so.
The more subtle change I've noticed over the past ten tests or so is that there will be a few correct answer choices per RC section that stretch a little farther from the explicit text of the passage than older RC tests ever dared to do.
Again, though, this means that 2 or 3 of the 26 questions will be slightly harder/looser than they were in the past.
LOGICAL REASONING -
In older tests, you'll see more "2 for 1" questions: one stimulus, with 2 questions asked about it. That's probably a bit of a time-saver, since you don't have to read the stimulus for as long to answer the second question. So, since modern LR sections don't have those "2 for 1" questions anymore, they may feel slightly harder to finish in time.
One other subtle difference - older tests are more likely to revolve around some of the signature LSAT "recurring flaws" (of course, in the early tests, they were just OCCURRING, not RE-CURRING). Once the test taking nation became wise to LSAT's patterns, LSAT started using those recurring flaws more as trap answers.
So modern tests will often deliver the usual flaws and usual answer choices on easier questions, but it will sometimes do a "bait-and-switch" on a harder question that preys upon our knowledge of their recurring flaws. So you might read something that looks like classic "Absence of Evidence" but find that there is no answer choice that describes the flaw how they normally do. These questions test/reward flexibility.
Again, though, we're talking about 2-3 questions per test that are sort of using our knowledge of past tests against us.
Some tests just have particularly hard sections, whether it's an RC, a Games, or one of the two LR's. Remember that the difficulty of a test is supposed to balance out across all 4 sections. So if you see a really hard LR section, you might not want to attribute that to "modern LR sections" but rather just recognize that the other 3 sections from that test are likely to be relatively normal if not easier.
So, I am not at all concerned about people using older tests to prep. Certainly it's better to do the majority of your full-length timed tests with the most recent material; but I think that 90% of the older tests is true to form nowadays, so it's still an extremely useful reservoir of LSAT material.