Real op-amps approximate the ideal model only over a limited operating range.

The output voltage cannot exceed the available supply rails, and the output current is limited. Inputs also have a permitted common-mode range; operating outside it can invalidate the expected differential-amplifier behavior.

Open-loop gain decreases with frequency. As a result, a closed-loop amplifier has finite bandwidth, and higher closed-loop gain generally leaves less bandwidth available.

The slew rate limits how quickly the output voltage can change:

$$\left|\frac{dv_o}{dt}\right|\le SR.$$

Large, fast signals can therefore distort even when their frequency lies inside the small-signal bandwidth.

Input offset voltage, bias currents and noise create additional errors in precision circuits.

The ideal rules $i_+=i_-=0$ and $v_+\approx v_-$ are therefore design approximations, not universal physical identities. A circuit must also satisfy supply, input, output and dynamic limits.