Minor impurities should not cause any trouble. Also, if you only use small amounts of solvent infrequently, it is OK to discard it.
Having said that, here's a general tek for purifying n-Heptane:
1. Freeze the heptane as deep as you can and decant it off any impurities that precipitate. Use a closed container to avoid water vapor condensation. For best results you can use a cooling bath with dry ice in dry alcohol, or use a medical freezer.
2. Transfer the heptane to a separatory funnel. Slowly add concentrated H2SO4. Shake the mixture, allowing any pressure to escape. If the acid phase changes its color - discard and replace it. Repeat the washes until the acid phase remains colorless for several hours. Discard the acid phase, wash the heptane with distilled water, then with 2N NaOH, then with distilled water once again.
3. Dry the heptane over 4Å molecular sieves (10-20% m/v). Perform a fractional distillation. Increase the heat slowly and discard anything that distills out before the vapor temperature at the condenser stabilizes at the boiling point. End the distillation when it finally slows down and discard the remaining higher-boiling impurities.
4. Repeat step 3 one more time.
Optionally, when you first purchase your heptane you can test it for alkene impurities. To do that, wash some of it with a cold dilute alkaline solution of KMnO4. If the purple color of KMnO4 darkens to brown (due to MnO2 in suspension) it means you had alkene impurities and have now washed some of them out. If the purple color of KMnO4 does not change then your heptane is, and will most likely remain, free of alkenes.