Q:

Transistor biasing, Large Resisor values

simulate this circuit – Schematic created using CircuitLab
In above circuit the base of Q1 acts as a level-shifter from 3V-50V at it's base to 2.8V. The base of Q1 is driven by PNP open-collector outputs thus R2 holds the Q1 in it's off-state when the input signal is not asserted. The output pull-up can be rather large (22k) since speed is not too important but power-consumption is.
This gives a collector current of:
$$ I_{C(min)} = \frac{2.8\mathrm{V}}{22\mathrm{k\Omega}} = 0.13\mathrm{mA} $$
This leads to a small required base current, even when underestimating the current gain and providing a 30% error budget:
$$
h_{FE(min)} = 100 \\
V_{BE(sat)} = 0.75\mathrm{V} \\
I_{B(min)} = 1.3 \frac{I_{C(min)}}{h_{FE(min)}} = 0.0017\mathrm{mA}
$$
As noted above the input voltage at the base relative to ground is in the range of \$V_{in(min)}=3\mathrm{V}\$ to \$V_{in(max)}=50.4\mathrm{V}\$ which imposes the following restrictions on \$R_B\$:
$$ R_{1(max)}   = \frac{V_{in(min)} - V_{BE(sat)}}{I_{B(min)}} = 1.3\mathrm{M\Omega} $$
According to those calculations \$R_1=1\mathrm{M\Omega}\$ and \$R_2=10\mathrm{M\Omega}\$ would be sufficient. 
However, I wonder whether there are any drawbacks choosing resistors in the Mega-Ohm range for transistor biasing.

A:

Two drawbacks come to mind:
Firstly, noise. Two kinds really, thermal noise and shot noise. However, if the transistor is being driven into saturation, noise performance is probably not in your list of considerations. If you were making a linear amplifier however, it could be.
Secondly, switching speed. The base is not without capacitance. The Miller effect effectively amplifies this capacitance. Driving the transistor hard into saturation results in storage delay. There are various methods to reduce these slownesses, but all of them are made more effective by driving the base with a lower impedance, which a resistor in the megaohm range isn't. However, slow may not be a problem for your application if slow is fast enough.

