If Venus was entirely inside the habitable zone, or life zone, would its proximity to the Earth provoke any remarkable changes to the Earth?
One option would be a co-orbital scenario, which is described in more detail here. The latter would allow Earth and Venus to stay both in the habitable zone. But the effects for Earth could be very remarkable in some cases: Seasons would change over time, since eccentricity of Earth's orbit would change. If Earth and Venus would follow a horseshoe orbit, we would get variations in the length of a year.
Co-orbital systems can become instable by the gravity of other planets.
In the long run tidal forces may lead to a collision of the two co-orbiting planets.
Changes on Earth:
Except for possible tides and possible eclipses, if it were near enough, no.
Changes on Earth's orbit:
Venus would establish some resonance with Earth's orbit, if it were near enough or in one of the exact possible spots. This will not have a major impact except on year's lenght and Sun illumination on Earth.