RDHNTR - I've been shooting Rem 700's as my primary hunting rifles, and also in some target competition since 1974. That's 30+ years of shooting the darned things in many different configurations. Still have that original rifle too. My favorite deer & coyote rifle isn't much different from yours; a 700 CDL in .25-06 Rem. It's worked out real well.
Good - they are often pretty darned accurate right out of the box. Not at all unusual for a sporter weight Rem 700 to shoot MOA or better with decent ammo. The varmint weight rifles often do considerably better.
Another good point about Remington 700's is that they have been so popular, for so long, that a huge variety of aftermarket parts is available. A lot of gunsmiths have also made a career out of building highly accurate varmint or target rifles from the Rem 700, and know how to make these things really sing.
Bad/Ugly - there have been issues with the safety/trigger mechanisms - I've seen a Rem 700 fire when the safety was flicked off, and there was no finger on the trigger... Not good. I do believe though that in that case, the trigger had been worked on by someone who thought they knew what they were doing.
Sometimes the ejector can get stuck back inside the bolt face. This is usually pretty easy to fix and doesn't happen often.
Sometimes the extractor breaks - I've had this happen exactly once in 30+ years of shooting the darned things, including one rifle that has gone through several .308 barrels. It happened on the 6th shot from a brand new .300 Rem Ultra Mag. Remington promptly shipped me the repair part for free and I was back in business with that rifle in a few days.
Often the factory barrels have a very generous chamber, with a long jump to the rifling. This can cause some consternation for handloaders, but I've found that Sierra bullets generally tolerate the jump to the rifling quite nicely, and good accuracy is the norm even if the bullet has to jump half the length of a football field to engage the rifling...

I don't see it as much of a problem, but some folks get all worked up about it.
Any other issues? Let me know, I've used these things in some very harsh conditions and they continue to impress. Worth remembering that the U.S. Army uses sniper rifles built by Remington - and that they perform rather well in tough conditions. Most LE agencies also use sniper rifles built on Remington 700 actions too.
Regards, Guy