If you are getting message errors about the client.dll file check if you have at least Half-Life version 1.1.0.0. Azure Sheep needs at least that version to run.

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When using lifts that have doors if a door is blocked the lift may not work properly. To fix that load a game that you saved before using the lift.

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Sometimes the doors don't open because of a dead monster near them. To fix it explode the monster.

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Sometimes Kate doesn't follow the player. This happens because Kate can't find a path to follow the player. To fix this try to rehire her again or to walk against her so she moves out of your way and by doing that going to a place where she can find the path to follow you.

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Sometimes Kate don't walk across an area because there is a dead monster in the way. To fix it explode the monster.

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In the second map of the 'LAST STEP' chapter, the Special Force that jumps the wall very rarelly may became imune to bullet fire. To kill him just blow him up.

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Kate elevator squish bug.
You need to do this to bypass the bug:

1- Start Half-Life from the DOS Prompt with the command: hl -dev -console
2- Choose Azure Sheep and load the saved game you have where the bug occurs
3- After Kate finish typing the buttons keys and turn bring down the console (usually by typing the ~ key) and type: sv_gravity -100
4- Kate (and you if you jump) will start floating to the ceiling
5- When the elevator is almost at the top bring down the console again and type: sv_gravity 800
6- Normal gravity will be set again and Kate will fall and will get out of the elevator.

After you bypass the bug you may save the game, exit Azure Sheep and reload Half-Life as you always do. This solution may not work at the first try but it will work sooner or later if you keep trying.
Thanks to Zac Durham for giving a solution to bypass this bug.

Kate elevator squish bug solution 2.
For those who already killed all the enemies in the problematic map and the next and the only thing that keeps you from entering the jeep is Kate being squished on the elevator, there is a easier way for you to be able to bypass the squish bug and finish Azure Sheep (by entering the jeep). Azure Sheep as a impulse command that makes a Kate appear near the starting area of a map. This command was created during the development of the mod and it can give allot of problems if not used correctly. For example, the Kate that will appear doesn't end the game when killed or, when you have two Kates on the same map they will not do what they have to do (including using retina scanners). So, again, if you already killed all the monsters and just want to see the ending go to the last map (the one where you have to get into the jeep) and type 'impulse 77' in the console (without the '), a Kate will appear near the starting area of the map and you may use it to follow you to the jeep and end the game.

Kate elevator squish bug solution 3.
This solution may not work for everyone but, if you don't do that already, let Kate use the elevator alone and you use the stairs to climb to the top.

Kate elevator squish bug solution 4.
This may not work for everybody but if you are using OpenGL change to DirectX and see if Kate is squished. You may always return to OpenGL after Kate comes out of the elevator.
Thanks to Steve McDermott for the info.

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Azure Sheep doesn't run. Check if you installed Azure Sheep how is in the dir.gif file.

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When starting a game Azure Sheep doesn't find the maps. Check if you installed Azure Sheep in a directory with spaces on the name, like 'Azure Sheep'.
Half-Life doesn't supports mod directories with spaces between. To solve it rename the directory to 'asheep' or 'AzureSheep' (without the ').

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"Kill all enemies first...". When you try to go to the jeep this message appears, what you have to do is to kill all 12 Special Forces and the 2 Apaches located only in that map (the 2nd Apache will appear after you kill the first). No need to go to the previous map to kill all the enemies there. You will have to look for the Special Forces because some (at least 1) will not go after you. If you did this already and know that everyone is killed then reload a previously saved game and try again...

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In the second map of Azure Sheep the Apache needs to crash on the ground making the pickup truck to blow. If this doesn't happens load a previously saved game and try again.