Electronic – Contact resistance is messing with the transistor switch

First, why do you think you need a digital signal that goes high when the switch is pressed? In a lot of cases, such a digital input signal can be dealt with being any polarity as long as it is known. If this is going into a microcontroller or FPGA, for example, then it's just as easy to use a low going pulse to indicate pressed as a high going pulse. Explain what you need these digital signals for. Quite likely tying the common of the switches to ground with a simple pullup on each switch to the supply is all you need if the rest of the system is thought thru properly.

If you really really need the pulse to be positive, there are various options. One conceptually simple way is the common ground and then pullup for each switch, but feed that into a CMOS inverter, preferably one with Schmit trigger inputs. CMOS inverters take effectively no power when sitting in a particular state, so no power will be consumed unless a switch is pressed.

If you want to do it yourself from discrete parts, here is one way:

OUT will be normally low and go high when the button is pressed. You can make R1 smaller depending on what impedance you need OUT to be. 10 kΩ is fine for most logic inputs, but you could make it 1 kΩ if you needed more low-going drive at the cost of higher current when the button is pressed. Since one side of the button is at ground, all your buttons could be hooked up similarly, each to their own circuit, with the common plate to ground.

If it were me though, I'd probably use the CMOS inverter method. Actually I'd use the low-when-pressed polarity first, then use the CMOS inverter method if I really needed high-when-pressed for some unusual reason.

The major limit to BJT switching time is related to the charge carriers and specifically how long it takes to move carriers into the base, and how long it takes to get them out.

The datasheet will include a few parameters that will give you the theoretical maximum switching frequency*. They are

1. Delay time (td) - how long it takes to get out of cutoff
2. Rise time (tr) - how long is the transition from cutoff to saturation
3. Fall time (tf) - how long is the transition from saturation to cutoff
4. Storage time (ts) - how long to get out of saturation

Using the datasheet (these parameters are usually listed), you can figure out how fast a transistor can switch between the two states.

$$ f_{max} = \frac{1}{t_d + t_r + t_f + t_s} $$

* This is what transistor can theoretically do, but there are tricks that can be done to improve the switching speed. Also, if you are switching a square wave, then in order to maintain a nice square waveform, the actual switching frequency will be much less.