Here is a simple and affordable solution to troublesome thresholds.  Smooth out the transition with one of these nosing ramps from Diestco. This is useful for smoothing a threshold for people who use a wheelchair and also people at risk for tripping. They are constructed of soild rubber making them easy to install. They can be modified with a saw to fit around molding and tight spaces. Available in 3 sizes up to 1.75". Recommended for residential use only.

Small 3/4" x 2 3/4" x 36"
Medium 1 1/4" x 4 1/4" x 36"
Large 1 3/4" x 5 1/2" x 36"