Basicly magnetic field is there only because of space contraction (which comes from Special Relativity). E/magnetic (light, radio, x-rays, etc) - due to 2 reasons: space-time invariance (again SR) and inertia (mass) of electric field (m=E/c^2). So, if you ever used electricity, radio, or ever started a car (with DC start motor) - then you were directly using results of existence of Special Relativity.
If SR is incorrect, then practically everything related to electricity instantly falls apart. Generators and alternators won't generate electricity, transformers won't transform, motors won't run, computers won't compute. E/m radiation will not exist, so no sunlight or any other starlight would exist, and no radio would exist either.
Not to mention that accuracy of Einsteinian SR equations were verified to extremely high degree using accurate clocks on board of space vehicles, and especially in accelerators where electrons move with 99.9999% speed of light. Basicly, accelerators built without correct SR equations in their design are completely useless - rising mass of particles (with their speed) requires special acceleration techniques.
GR (general relativity)is also verified experimentally to high accuracy. The prediction that the speed of gravity equals to the speed of light is verified to better than 99% accuracy observing spiraling binary beutron stars.
Gravitational time dilation (red/blue shift) is verified with much better accuracy using so called Moessbauer effect and using very accurate atomic clocks (clocks in Washington DC runs slower than in Boulder, CO due to lower elevation (more g) and in exact agreement with Einstein GR equations.
If you ever used GPS system, then it will be interesting for u to know that the receiver is constantly correcting satellite atomic clocks due to their motion (SR equations correction) and due to difference in elevation (different g near receiver versus near satellite causes different time dilation due to GR). Without relativistic effects correction the receiver gets lost with the speed about 0.7 ft/sec, or about 10 miless off per day.
So, today I would not insist much neither on incorrectness of Einstein theories nor on their uselessness.