No need to bring any kind of common sense, mind. It'd only slow us down.
Harkonnen patrols are common in the cities. They typically consist of 4-6 soldiers with an NCO leading them. They will be armed with kindjals, maula pistols and laspistols.
A city fremen trying to make a living by picking pockets. If the characters are desert fremen carrying crysknives, the pick pocket may try to steal one to claim the substantial reward.
If the character party is made up of desert fremen with at least one woman, then they could encounter one of Chulo’s snatch squads, looking to take a desert woman alive. Note that they will try to take any women alive, preferably without any wounds, but won’t care whether or not any men live.
Count Fenring, Lady Margot Fenring or a member of a Major or Minor House may all be encountered on the streets of either city, with accompanying guards. Count or Lady Fenring may be guarded by Sardaukar.
If the characters are desert fremen, they may have to make a delivery of spice to the Guild, since the fremen bribe the Guild to keep satellites out of the skies. The delivery could be made to Jasta Mason.
If the characters are not desert fremen, they could happen upon such a delivery.
Arrakeen and Carthag are both very poor cities, so there are beggars. Anyone who looks relatively wealthy and/or generous/gullible is likely to encounter beggars asking for money or water. The beggars may be quite aggressive, but will have little or no combat ability and no weapons.
Smugglers harvest spice to sell on the black market. The characters could encounter them in the desert, while they are harvesting. They should be equipped with good quality stillsuits, kindjals and laspistols or maula pistols.
Spotter ornithopters routinely fly over the desert, searching for spice blows to be harvested. Anyone in the desert has a chance of seeing such a spotter, and of being seen by the spotter.
A spice harvester, working the sands. There will be spotters nearby watching for wormsign. Alternatively, a wrecked harvester (wrecked by worm or storm) could be found.
If the characters are desert fremen, they should be able to detect the oncoming storm in plenty of time to take shelter. If they are not desert fremen, they may struggle to find shelter, and are unlikely to survive in that case.
This is a person deposited in the desert by the Harkonnen to die. Optionally, the person may be wearing a pseudo-shield. In this case, they will attract at least one worm, possibly several. Having been driven into a frenzy by the pseudo-shield, if there are multiple worms they will attack each other.