With the discovery of new superconducting materials, such as the iron pnictides, exploring their potential for applications is one of the foremost tasks. Even if the critical temperature T(c) is high, intrinsic electronic properties might render applications difficult, particularly if extreme electronic anisotropy prevents effective pinning of vortices and thus severely limits the critical current density, a problem well known for cuprates. Although many questions concerning microscopic electronic properties of the iron pnictides have been successfully addressed and estimates point to a very high upper critical field, their application potential is less clear. Thus, we focus here on the critical currents, their anisotropy and the onset of electrical dissipation in high magnetic fields up to 65 T. Our detailed study of the transport properties of SmFeAsO(0.7)F(0.25) single crystals reveals a promising combination of high (>2 x 10(6) A cm(-2)) and nearly isotropic critical current densities along all crystal directions. This favourable intragrain current transport in SmFeAs(O, F), which shows the highest T(c) of 54 K at ambient pressure, is a crucial requirement for possible applications. Essential in these experiments are four-probe measurements on focused-ion-beam-cut single crystals with a sub-square-micrometre cross-section, with current along and perpendicular to the crystallographic c axis.