Although most of the solar surface outside active regions (ARs) is pervaded by small-scale fields of mixed polarity, this magnetic "carpet" or "junkyard" is thought to be largely absent inside AR plages and strong network. However, using extreme-ultraviolet images and line-of-sight magnetograms from the Solar Dynamics Observatory, we find that unipolar flux concentrations, both inside and outside ARs, often have small, loop-shaped Fe ix 17.1 and Fe xii 19.3 nm features embedded within them, even though no minority-polarity flux is visible in the corresponding magnetograms. Such looplike structures, characterized by horizontal sizes of ~3–5 Mm and varying on timescales of minutes or less, are seen inside bright 17.1 nm moss, as well as in fainter moss-like regions associated with weaker network outside ARs. We also note a tendency for bright coronal loops to show compact, looplike features at their footpoints. Based on these observations, we suggest that present-day magnetograms may be substantially underrepresenting the amount of minority-polarity flux inside plages and strong network, and that reconnection between small bipoles and the overlying large-scale field could be a major source of coronal heating both in ARs and in the quiet Sun.