This is a commonly asked question because when people first notice the discrepancy, it can be confusing. So, let’s clear this up.
Watch makers didn't make a mistake and include the wrong Roman Numeral on the dial. "IIII" has been used instead of "IV" on dials for several hundred years. It’s really a matter of aesthetics and visual symmetrical balance. Hundreds of years ago, someone noticed that using “IIII” for 4 o'clock not only made the dial look better, but helped legibility when looking at the dial from different angles.
It’s called a "Watchmaker's Four," and it is used for those reasons.
Many clocks use “IIII” because that was the tradition established by the earliest surviving clock, the Wells Cathedral clock built between 1386 and 1392. It used “IIII” because that was the typical method used to denote 4 in contemporary manuscripts (as iiij or iiii). That clock had an asymmetrical 24-hour dial and used Arabic numerals for a minute dial and a moon dial, so theories depending on a symmetrical 12-hour clock face do not apply.
Perhaps IV was avoided because IV represented the Roman god Jupiter, whose Latin name, IVPPITER, begins with IV. This suggestion has been attributed to Isaac Asimov.
Also, Louis XIV, king of France, who preferred IIII over IV, ordered his clock makers to produce clocks with IIII and not IV, and so it has remained.
Using standard numerals, two sets of figures would be similar and therefore easily confused by children and others unused to reading clock faces: IV and VI are similar, as are IX and XI. As the first pair are upside down on the face, an additional level of confusion would be avoided by using IIII to provide a clear distinction from VI.
The four-character form IIII creates a visual symmetry with the VIII on the other side, which the two-character IV would not.
With IIII, the number of symbols on the clock totals twenty Is, four Vs, and four X’s, so clock makers need only a single mold with a V, five I’s, and an X to make the correct number of numerals for their clocks: VIIIIIX. This is cast four times for each clock and the twelve required numerals are separated:
V IIII IX
VI II IIX
VII III X
VIII I I
The IIX and one of the IXs are rotated 180° to form XI and XII. The alternative with IV uses seventeen I’s, five V’s, and four X’s, requiring the clock maker to have several different patterns.
Only the “I” symbol would be seen in the first four hours of the clock, the V symbol would only appear in the next four hours, and the X symbol only in the last four hours. This would add to the clock's radial symmetry.