Hi Tulips,
Yes, bad furniture arrangement be result in bad feng shui and cause money, health or relationship problems. However, not everything is important in the house. Most of what you've probably heard are "pan-tang" or "new age" feng shui, which has no logic..
In authentic feng shui, the main door, the stove positioning, the bedroom, the bed position as well as the water feature placement (eg fish tanks or water fountains) are the most important. If you can get all these correct, normally your house feng shui cannot be that bad (without considering the external environment in this case).
The clock facing will not affect the feng shui of the house in any way , so not to worry. The only type of clocks that might affect are those cuckoo clock, grandfather clock with large swinging pendulums, or clocks that has a loud alarm/bell that rings every hour. If they are placed in an area with negative Qi, it will trigger those Qi, and what problems you will get will depend on the Qi in that sector.
If your clock is a normal clock without any alarms etc, you can hang anywhere you think it looks nice and asthetic. Not to worry