If we ignore the giant impact (which would have enormous effects), and just look at the effect of the Earth having a 0 degree axial tilt, the most immediately apparent effect is that the seasons would be reduced almost to nothing and the very small seasons that remain would be planet wide, not alternating between the 2 hemispheres.
The Earth is currently closest to the sun in the first week of January and furthest in the first week of July. Source, so it's pretty obvious that being closer to the sun doesn't create summer. The axial tilt is what causes the seasons, but the change in distance to the sun still has some effect.
There's a little over 3% variation in distance, see source, yielding a bit over 9% variation in energy received between the Earth's perihelion and aphelion, but that doesn't mean a 9% change in temperature. It's much smaller than that due to the Earth's oceans, atmosphere and to a lesser extent, surface are all heat sinks that take a long time to warm up or cool down. The seasonal difference in temperature would be much less than that. Maybe a few degrees, perhaps 5-10 degree difference between summer and winter, probably less than the change between night and day.
No tilt also means, you lose the 6 months of sunlight, 6 months of darkness that we currently get near the poles and the sun wouldn't be higher in the sky in summer than in winter. At the poles, you'd effectively get sunset, 24 hours a day, 365 days a year but over most of the Earth you'd have 12 hours (and a few minutes) of sunlight and nearly 12 hours of, not darkness, cause you'd still have twilight and dawn, but over the most of the planet, it would be 12 hour days pretty much.
The poles would receive less solar energy and could be colder and there wouldn't be a spring thaw or summer growth. Plant Growth would be pretty consistent all year around.
The equator would have more peak sun and could be hotter. With our current tilt, the pole to equator solar energy ratio is 0.4 to 1. Source. With no tilt, it would be 0 to 1. The poles could see an increase in permanent ice.
But, despite that increase in ice, you'd get a decrease in solar-ice-reflection, so that could mean a warmer earth, even with more ice on both poles. The equatorial region could be hotter.
Circulation is hugely complex, so that's a great big wild-card. Seasonal driven ocean and air currents would be greatly reduced but temperature driven currents should increase, though the reduction of temperature variation is difficult to predict. You still get night to day temperature variation, but the overall effect on wind and ocean currents is too hard for me to predict.
Hyper-physics says the tilt is essential to life (linked above). I'm not sure that's true, but no seasons and potentially reduced circulation due to more consistent temperatures could have a pretty big effect. The potentially worst outcome could be a significant still water in the oceans which could create large dead zones. That's by no means a certainty, but it's possible.
Article on the effects of the ocean conveyor belt stopping, if interested.
If I missed anything, comments are welcome.