Is there any disadvantage to changing trace width in the middle of a trace?
Yes, but these disadvantages may be negligible.
Disadvantage 1: High frequency signals encounter a discontinuity.
I would start worrying at a few hundred megahertz because the change in trace width changes the characteristic impedance (not just dc resistance) of that line. The discontinuity changes scattering parameters, creates harmonics, reflections, and other headache-inducing problems.
Disadvantage 2: Voltage drop (and increased power dissipation) due to higher trace resistance.
If the decreased-width percent of the trace is less than 10%, I wouldn't worry. All of these effects can be calculated for your potential design, however.
Here's an online tool that helps estimate trace resistance
Here's a downloadable tool that has a lot of built-in equations
For one thing, many PCB layout programs will allow, or automatically incorporate, "necking" of traces due to unconnected pads or keep-out areas. This is a reduction of trace width for a portion of the trace.
There are some concerns with such trace width reduction:
If the reduced trace width is over an extended distance, then the increased resistance of the narrower trace will give rise to more heat, and will dissipate generated heat less easily, than the wider trace. For brief neck sections, this is not so much of a concern, as the heat gets conducted out to the wider traces on both sides of the neck.
The narrowest trace width is the one determining how much current can be borne by the trace. If the narrow trace is still wide enough, then for moderate signal frequencies it isn't a major problem to have the trace equally narrow throughout, instead of having wider sections at all.
Signal impedance and signal reflection issues as pointed out in comments and other answers - specifically for higher frequency signals.
If your are dealing with high frequencies ( around 100 MHz and above ), it will definitely matter. The change in trace width will be seen as a discontinuity, causing mismatch and ultimately resulting in unwanted reflections. You will see its effect on the timing edges and hence the digital I/O levels.
EMI would depend upon the layout routing and the isolation ( or rather lack of adequate isolation ) between adjacent traces. Stripline Vs Microstrip.
For low frequency operations, the major factor to take cognizance is the amount of current carried by the trace and heat. The safe current carrying capacity of the trace is determined by the narrowest section of the trace.
From the data you provided, using 50 mils trace...it seems like you are planning for a high current application. For a standard FR4 1 oz copper, 20 mils is good for 1A ...stripline routing . Others sometimes use thick traces for robustness in production.