Using the /summon command with the ActiveEffects NBT tag to create a mob with effects will spawn it with the given effects, but some do not work properly. I've tested Speed, Slowness, Strength and Weakness. In all cases, the potion particles appear and the mob is treated as having the effect with the given amplifier when throwing a splash potion at it.

Using the command

/summon minecraft:zombie ~ ~ ~ {ActiveEffects:[{Id:1,Amplifier:4,Duration:9999}]}

will spawn a zombie that displays the expected light blue speed particles, but moves at the same speed as a normal zombie spawned without the effect. Throwing a splash potion of swiftness level 2 at the zombie summoned by the command does not affect it, while throwing the same potion at another, effect-less zombie noticeably increases its speed.

The same can be observed with the slowness effect, and also with strength and weakness. Using the command with a high strength or weakness effect creates a zombie that will always require the same amount of hits to kill a villager. Other effects like levitation do work, so I suspect the bug has something to do with attributes.

Edit: The same appears to happen with Spawners. Using the command

/setblock ~ ~1 ~ minecraft:spawner{SpawnData:{id:"minecraft:zombie",ActiveEffects:[{Id:1,Duration:10000,Amplifier:4}]}}

creates a spawner that spawns zombies with the broken speed effect.