Should I validate transactions using the rules in BIP62?
Yes, you should.

BIP62 is currently not being pursued as a consensus rule on the network.

However, all its rules (including the ones that are only applied to new style transactions according to BIP62, specifically the lower-S rule) - are currently being enforced as a standardness rule since Bitcoin Core 0.11.1 and 0.10.3.

The reason for this is that at the time BIP62 was written, requiring lower-S was not feasible due to the large amount of wallets that were still creating high-S signatures. In recent times, a large fraction of them switched to lower-S, making it viable to just unconditionally apply that rule. If a significant amount of network nodes (and specifically, miners) upgrade to versions that enforce this, wallets that do not enforce lower-S will gradually stop working and need upgrading.

If that process completes and we end up in a state where near-0% of blocks still contain high-S signatures, people may want to propose unconditionally applying it as a consensus rule.