Are alternate connection points on a PCB bad?
A truly definitive answer might be too long, so I will try to highlight some of the concerns rather than be comprehensive.

First, for high speed digital or sensitive analog signals, it is best to avoid this practice. High speed traces suffer signal degradation if there are long stubs. For inputs (for example a microphone input), long traces can become pickup antennas for low level noise. This will normally not be a problem for slow (&lt;1 MHz) digital or full swing (rail-to-rail) analog. Examples of signals I would NOT fork are ethernet, USB, or microphones. It would be catastrophic for an RF antenna also. You cannot put random forks into RF feeds.

Barring that, there are mostly system level design issues. The kind of things to consider are how easy would it be for someone to accidentally use both interfaces, and if they did, would that be a problem? For example, if one of the connections is a power input, is there a possibility that someone would connect two different power supplies at the same time? Would that be bad? You would, in effect, be shorting together two external power supplies using the traces on your PCB.

If it was an audio input, and someone might hook up different audio signals to the two different inputs, would that harm one of the audio sources?

The situation for signal outputs is less problematic, as long as they are not too high speed, as previously mentioned, there is not likely to be any problem if you send a signal to two different receivers at the same time.

For signaling systems that are inherently robust, even when two outputs are connected together, such as RS232 or any type of open-collector based system, there is little potential for harm. RS232 is supposed to be designed so two outputs can be connected together indefinitely without permanent damage. So there is not too much danger there. A lot of so-called RS232 interfaces are now really TTL level devices and may not be as robust.

A lot of serial communication schemes use open-collector outputs. I2C for example. No danger with that. It just won't work properly if things are not connected in sane fashion.

There is one more thing to watch out for. It is not exactly related to your question, but it is similar. If you have a digital input and there is no output driving it and there is a long trace, that input needs a reasonably strong pullup or pulldown to avoid accidental switching. Or, you can use a capacitor in conjunction with a weak pullup or pulldown. Otherwise a nearby voltage spike might couple in by way of the trace and cause unintended switching.