The Fundamental Problem
Naturally the specifications the parts in the system in question and what is considered "acceptable error" for the system will both change the exact limits, but is there a single order of magnitude in time, or distance that I can expect dead reckoning to work? I'm well aware that over long distances (a few yards or so) the error becomes too large for most practical purposes, but what about within a few feet?
This can be addressed by studying the short term error dynamics of an inertial navigation system. It's covered in detail in many texts, but here's the short "equation free" version.
Inertial navigation works as follows:
Precisely know your initial position, velocity and attitude (i.e. pitch roll and yaw).
Integrate the output of your gyroscopes (angular rate) over some short period of time \$\Delta t\$ to get an increment of pitch, roll and yaw and add them to your current attitude.
Use your new attitude you just calculated to mathematically rotate your accelerometer readings to be level with the earth.
Subtract gravity from your newly-level accelerometer readings.
Integrate your accel-minus-gravity measurements over a short period of time \$\Delta t\$ to get an increment of velocity. Add this to your current velocity.
Integrate your newly calculate velocity over a short period of time \$\Delta t\$ to get an increment of position. Add this to your current position.
Repeat steps 2-6 for as long as want.
Suppose your gyro has some error on it - for example, a bias \$b_g\$. The error will get integrated once for attitude, integrated again for velocity then integrated again for position. Thus, that error grows with \$ b_g \times \Delta t \times \Delta t \times \Delta t = b_g (\Delta t)^3 \$ from one time step alone.
Furthermore, that bias will accumulate into attitude, which will cause the accelerometers to be leveled wrong, which will cause the acceleration to be leveled in the wrong direction, which will then be integrated into the wrong direction - three tiers of errors.
This means that gyro errors cause position errors to grow with the cube of time.
By the same logic accelerometer error cause position errors to grow with the square of time.
Because of this, you'll get mere seconds of useful (pure) inertial navigation from mobile-phone grade MEMS sensors.
Even if you have extremely good inertial sensors - say, aircraft grade - then you are still fundamentally limited to slightly under ten minutes of (pure) inertial navigation. The reason is Step 3 - gravity changes with height. Get your height wrong and your gravity will will be wrong, which causes your height to be wrong, which causes your gravity to be more wrong and so on - exponential error growth. Thus, even a "pure" inertial navigation system such as those found in military jets will usually have something like a barometric altimeter. Source.
Additionally, a general consensus seems to the only way to improve these limits past the point of improved sensors is to provide a reference not subject to error.
Even if you have a reference attitude (e.g. magentometer to provide heading, and something else to provide accurate pitch and roll), you will still be limited by the \$ t^2 \$ error in accelerometers. Thus, some sort of positioning is necessary.
Some systems solve this using cameras and markers. What kind of reference points can a portable/wearable device provide?
There is both research and commerical products that can do this.
Conceptually, it works like stereo vision - you have a known baseline between cameras, and a different angle to each marker as viewed from each camera. From this, the 3D position of each mark can be computed (relative to the camera). It can work better with more cameras.
I've seen the usage of radio waves to measure long distances accurately, but I can't tell if such a system could be accurate on such small scale (in terms of distance measured) using "off-the-shelf" components.
Using cheap hardware, decawave UWB might be of some use (10cm ranging or so). You'll need to come up with your own algorithms through.
I know over longer distances a GPS can be used, but I doubt any consumer electronics grade GPS has fine enough resolution to help in my case.
Next to the body, a GPS system will struggle. Getting cm-level GPS relies on continuous phase tracking of the (very, very weak) GPS signals, which is extremely difficult if the antenna is next to the body, and the body is moving around! For L1 only-systems - regardless which they are cheap or expensive - the tracking has to be for a very long time (10min+) and is thus impractical for this problem. A dual-frequency receiver might work sometimes, but these are really not cheap (thousands of dollars).