Here is a complete walkthrough of Mortimer Beckett and the Crimson Thief.
You'll begin at the Coffee shop. Collect the hammer that is next to the fence. The pruning shears are in front of the streetlight. If you approach the table, the waiter will greet you with house wine. While examining the table top, you'll notice a tear from the table cloth. Mortimer explains that something is engraved on the table surface and that the tablecloth needs to be removed, he says it's too inappropriate for him to do it himself. Leave the table. You'll also notice a balcony, but you need a ladder in order to reach it.
You can head to the car shop. The owner explains that his car parts are out of order and that his previous assistant made a mess. He wants us to put the car parts back in order. While you're at it, collect the screwdriver that is in front of the car window, collect the tablet that is on the back of the car, and collect the blank paper that is behind the shelf. When you enter the backroom, you can see the car parts and a book explaining each part. This puzzle can be very tricky, so I suggest using the Strategy Guide from the title screen. You're supposed to sort them based on the information the book tells you I believe. Once you completed that puzzle, the owner will thank you and give you his car key. Once you collect the car key, head back in the backroom and collect the pencil that is sitting on top of the shelf and collect the tweezers that are above the switch.
Head to the West Tower and use the pruning shears on the bushes to reveal the ladder. Collect that. Collect the oil can that is next to the left streetlight. Head upstairs and you'll notice a crack on the wall. Mortimer explains that there is a piece of paper stuck inside, but he needs a proper tool. Use the tweezers on the crack to receive the first piece of the ticket. Collect the wheel that is sitting beside the wall with the crack, and collect the crowbar that is next to the other wall. You'll also notice a binoculars station, but we need a coin in order for it to work. We don't have it yet.
Head back to the Coffee Shop and enter the car. Use the car key on the ignition switch to start the car so that you can move forward, accessing the manhole. Use the crowbar on the manhole to open it up. You can then enter the sewer. Collect the coin that is sitting on top of the pipe. You can then examine the running water. Mortimer says that there's an object inside that big pipe. We need to be able to stop the water. Exit the sewer and use the ladder on the balcony. Now you can climb up to the balcony. Use the hammer on the pot to break it, revealing the room key. Collect it.
Head back to the West Tower, go upstairs and put the coin in the coin slot. You can now use the binoculars. While examining, you'll notice some numbers on the roof of the airfield hangar. Mortimer writes them down in his notebook. They are 72559. You can examine the other areas too. Head back downstairs and use the room key on the locked door. You can now enter the thief's hideout. Collect the fuse that is sitting on top of the dresser. Collect the clock key that is on top of the shelf. Collect the pincers that are next to the dresser. Use the clock key on the clock to receive your next ticket piece. You'll also notice a chest, but you need to find a clue in order to solve the puzzle.
Head to the Airfield and approach the hangar. Enter the numbers 72559 from your notebook and the doors will open. Enter the hangar and collect the glove that is behind the cart. We now have another puzzle to solve. We have to free the valve. You'll notice the cart is missing a wheel, so put the wheel on the cart. You also have to power up the buttons by putting the fuse in the fuse box. In order to free the valve, you have to move the cart over to the propeller. Then you can click the red button to have the propeller hold it down. Then, move the cart back over to where it was before, release the red button and click on the green button to lift up the object and reveal the valve. Use the oil can on the rusted plate, then use the screwdriver to unscrew the screws, revealing another piece of the ticket. Head back out of the hangar and use the glove on the broken glass to retrieve another ticket piece.
Head back to the Car Shop, enter the backroom, and use the pincers on the nailed box to retrieve your final ticket piece. We just need to find the stolen artifact. We are officially done with this area.
Head back to the Coffee Shop and approach the table. Use the tablet on the wine glass. This will cause the wine to spill all over the tablecloth. The waiter explains that he'll clean up the mess in a moment. He then removes the tablecloth. Put the paper on the table. Then, use the pencil to copy the numbers on the piece of paper. Mortimer will then copy the numbers in his notebook.
Head back to the West Tower, enter the thief's hideout, and approach the chest. Solve the puzzle using your notebook. This will reveal the crossbow. Collect it and you are now done with this area.
Head to the Coffee Shop, enter the sewer, and put the valve on the missing valve spot. This will stop the water flow. Finally, use your crossbow on the box and you have just recovered the stolen artifact.
Now you are ready for the next destination! Head to the Airfield and board the plane.