A landmark with no published record
The Gaddafi Mosque is the building most often named when Dodoma’s sights are listed, and it is the one about which least is officially published. It is a large congregational mosque in the city, known universally by that name, and it is prominent enough that a driver will know it without an address.
Beyond that, the record thins out fast. Dodoma City Council publishes no tourist-attraction page at all, and no national body consulted for this page carries a description, a construction date, a capacity figure, a set of dimensions or any visiting information for the mosque. Figures and dates do circulate in travel writing; none of them could be traced to a source that states them on its own authority, so none are repeated here. If a number matters to you, treat the ones you find online as unsourced.
What a visit actually involves
It is a working mosque, not a museum, and whether non-Muslim visitors may enter is decided by the people there on the day rather than by a published policy. That means the only reliable approach is to arrive respectfully, ask, and accept the answer — which may be yes, may be yes but only to the courtyard, and may be no, particularly around the five daily prayers and on Fridays.
The ordinary conventions apply and are not negotiable: modest dress covering arms and legs, a headscarf for women, shoes removed before entering, no photography of people at prayer, and no entry into the prayer hall during prayers unless you are praying. These are the same rules that govern mosque visits on the coast and in Stone Town, where visitors meet them more often.
Being honest about the stop
For a traveller with a camera and half an hour this is an exterior — a big, striking piece of modern religious architecture in a city that does not have many landmarks. That is a perfectly good reason to drive past it and a poor reason to plan around it. It works as one element of a morning circuit of the civic quarter, alongside the parliamentary precinct, the central square and the cathedrals, and it is best seen with someone local who can say what is currently allowed.
The Dodoma guide explains why the city’s own sights are a half-day rather than a destination, and why the argument for coming to this part of the country lies north at the Kondoa rock art rather than in the capital itself.