How to tell if the Spy I killed is using a Dead Ringer?

I'm not sure I should be giving away my tricks, but...

Not all on hit/on kill effects are replicated by the Dead Ringer. Some things that could give it away are:

• No hit sound is played. It's unclear if this is intended or if this is a bug.
• Spies covered in jarate or mad milk remain visible as an outline. Technically, this applies to Spies who were recently underwater, but this effect is much more difficult to see than the other two.
• You can still run into a cloaked dead ringer Spy. This is particularly obvious as a class that is faster than Spy that is melee attacking (Scout, Medic, Powerjack Pyro, Steak Sandvich Heavy)
• Not all kill effects are replicated (as TidB mentioned)
• If a Spy is disguising when they cloak, the disguise puff of smoke continues its animation.
• If you hit them with a crit or mini-crit, the words "Critical Hit" or "Mini-Crit" will follow the Spy around for a few seconds.
• If they were stunned by or at the time of activation, the stun particle effect follows them around.
• If they are hit with fire and have a Spy-cicle equipped, the Spy-cicle's evaporation sound plays.
• Ragdolls from a Dead Ringer sometimes don't have the correct velocity and seem to just drop to the ground. This is much rarer than it used to be, but still happens.
• Dominations and revenges will be faked in the kill feed and sounds, but not in the scoreboard.
• Characters will not play their domination/revenge sound clips for a fake death, unless the server has the appropriate plugin installed.
• Spy killstreak scores still show up in the scoreboard as they only reset on real death.

Things that make seem like a Dead Ringer activated them, but may not be:

• Hitting a Spy disguised as your team with the Ubersaw will not grant you Uber, even if you kill them.

Take a look on this table in the row "unreplicated mechanics" that shows effects that don't apply as they would normally do.

Besides this, there are some classical signs the spy is still alive:

• Coating effects like Mad Milk and Jarate are visible as well as waterdrops.
• Watch out for vanishing ammunition packs (that are restoring the Spy's cloak time) and healthpacks.
• The Dead Ringer has a very distinctive and loud sound; but you'll only hear it if the Spy is still near you.
• It's possible that a faked death leads to you dominating the Spy twice.

All the listed answers above are correct, but I have one more:

You can see the spy's cloaked outline for a split second as his rag doll counterpart falls to the ground. Try looking for that.