Does this mean it would only be a problem when I am reading analog pins?
No, but it's
mostly a problem with analog readings. However, when you don't use pull-up/down resistors on your digital lines, it will cause problems there too. Digital pins configured as digital input are in a high impedance state, meaning they require almost no current to detect a logic high. Floating input pins will randomly show up as high or low, because capacitive coupling is enough to supply this very low current.
While you can almost always use pull-up/down resistors on digital pins, you should be able to circumvent this problem. However, it's much harder to use these resistors on analog lines because it can lower the input impedance of the measurement circuit, disturb the circuit under test, cause ADC input impedance mismatch etc. That's why analog sampling is more sensitive to this interference.
I have traces that are about 4.5 inches long and are thin (about 7 mils or so). I do use pull-ups but do you think that that distance could create some problems witht he readings?
My smallest traces are 10 mil, which is thin enough to route between 2,54mm headers, with some of them having lengths of up to 70mm. Don't really have problems, but of course i don't know on which speeds you work. I only use LF signals, not much more than a couple of kHz's at most (except SPI, which runs at 4MHz).
Anyway, whole lectures can be given on trace width and routing. E.g. making your traces wider can increase the capacitive coupling because there is more surface that can act like a charged plate. You can also have inductive coupling, especially on traces carrying power (e.g. digital drive pins). The whole crosstalk problem is dependent on trace geometry, trace length and distance, ground plane position, dv/dt of the signal, the dielectric constant of the PCB material etc. Fortunately, for LF signals you don't have to worry too much about this.
Given the scenario I described above, how necessary is a ground plane? (Or Just in general how necessary are they would you say?). Thanks
I always use some basic tricks in my PCB design, one being an adequately laid down ground plane. This is mostly to provide all components with a low impedance ground path, because i find a lot of problems on LF boards are caused by inadequate grounding. When using a ground plane, or just whenever you lay down ground traces, you need to make sure the current only has one 'way' to flow to the ground plane or the ground connection. When you use multiple connections you run the risk of creating circulating currents in your ground connection, leading to common mode problems.
I also always use a separate ground plane for analog components, which is connected to the main ground plane through a single trace. This ensures noise, circulating currents and common mode problems stay out of my analog section.