Astrologers are not being difficult when they ask for a birth time down to the minute. The chart's most sensitive features are the ones that move fastest, and the fastest-moving thing in a natal chart is the horizon. Understanding the rates at which different factors change tells you exactly how much precision you need and when a rounded time will not do.
Everything in a chart moves, and the useful question is how fast relative to the window of your uncertainty. A birth time you know to the minute makes every placement solid. A time you know to the hour makes the outer planets solid and the Ascendant questionable. A time you do not know at all leaves signs intact and houses gone.
These rates are not linear, which is what trips people up. The Ascendant does not move at a constant 1 degree per 4 minutes all day. Near the equator it is close to that, but at higher latitudes the ecliptic meets the horizon at a shallow angle and some signs take a very long time to rise while others flash past.
Houses depend on time and on place, and both have to be right. The Ascendant depends on which degree of the ecliptic is crossing the local eastern horizon, and that horizon tilts differently depending on how far north or south you are. Move from the equator to 60 degrees north and the same clock time produces a different Ascendant and a wildly different house structure.
This is why a birth time without a birthplace is only half the information. Someone who knows they were born at 3:15 PM but not which city cannot get a reliable Ascendant, because the same moment yields different angles at different latitudes. The further from the equator the two candidate places sit, the bigger the discrepancy.
Twenty minutes of error moves the Ascendant about 5 degrees. That is usually harmless unless a sign boundary or a tight aspect sits inside those 5 degrees. An hour of error moves it roughly 15 degrees, which can change the sign outright if the Ascendant is in the early or late part of one. Ninety minutes and beyond, and you should treat the Ascendant as unknown.
House cusps move with the Ascendant and Midheaven, so a planet sitting near a cusp can flip houses on a small timing error. This is why astrologers warn about planets close to cusps even with a good birth time. With a rounded time, every cusp is suspect.
A lot. The Sun's sign, the sign placements of Mercury through Pluto, and every aspect among the planets except those involving the Moon at a degree level. The Moon's sign survives whenever it held one sign for the full day. The phase of the Moon, meaning the angle between Sun and Moon, is roughly determinable from the date.
What does not survive: the Ascendant, the Midheaven, all twelve house cusps, every planet's house placement, and the placement of the Part of Fortune. That is a meaningful loss, but it is one category of information rather than the whole chart.
First, figure out how uncertain. A certificate that reads 4:30 AM when most records show round numbers might be rounded to the half hour. A note that says 'early evening' might mean a three hour window. Knowing the size of the window tells you which placements are at risk.
Second, read the stable placements as fully as you would in a timed chart. They are real and they carry weight. Third, if you need houses, choose a method deliberately and label it: a noon chart, a solar chart, or rectification. Each is a scaffold, and none of them converts uncertainty into fact. Astrology is a symbolic tradition and has not been validated by controlled study, so the honest framing is that these are interpretive tools, not measurements of anything.