The text for Mislead states (emphasis mine):
You become invisible at the same time that an illusory double of you appears where you are standing.
You can use your action to move your illusory double up to twice your speed and make it gesture, speak, and behave in whatever way you choose.
Other Illusion spells specify how real the illusion seems. For instance, Major Image states:
It seems completely real, including sounds, smells, and temperature appropriate to the thing depicted.
Physical interaction with the image reveals it to be an illusion, because things can pass through it.
What are the limitations of Mislead's illusory double?
Can it interact with the environment (e.g. open doors, pull levers)? Is it solid? Does it have weight (or can it be made to seem to have weight)? How can the illusion be revealed? Can the illusion be revealed?
First of all you shouldn't compare two different spells, even if they are from the same school of illusion.
The limitations of Mislead's illusory double are just as written:
Accordingly to Illusion school description, from Player's Handbook, page 203
Basically illusions are not real and therefore have no weight, they will not leave footprints and they can't physically react.
The one exception would be Creation spell, which uses shadow material from Shadowfell to create a temporary physical object.
Anything that counters illusions, would affect the Double as well. For example truesight or Mordenkainen's Faithful Hound.
Nothing says what would happen, if somebody tried to react with your double. Most probably they would realise, that they are dealing with a ghost or an illusion.