**Core Concept**
The question is testing the understanding of the adverse effects of intravenous administration of amide local anesthetics, specifically the risk of systemic toxicity. Systemic toxicity of local anesthetics is a serious concern when large doses are administered intravenously.

**Why the Correct Answer is Right**
The most important adverse effect of intravenous administration of large doses of amide local anesthetics is **cardiac toxicity**. This occurs due to the blockade of sodium channels in the heart, leading to a reduction in the rate of rise of the action potential and a subsequent decrease in cardiac contractility. The blockade of sodium channels also affects the conduction velocity in the heart, leading to a prolongation of the QRS complex. This can eventually lead to cardiac arrest. The mechanism of cardiac toxicity is related to the blockade of sodium channels by the local anesthetic, which can be exacerbated by the high concentration of the drug in the bloodstream.

**Why Each Wrong Option is Incorrect**
**Option A:** Other adverse effects of local anesthetics, such as central nervous system toxicity, are also important but not the most critical when administering large doses intravenously.

**Option B:** While methemoglobinemia is a potential adverse effect of certain local anesthetics, it is not the most significant concern when administering large doses intravenously.

**Option C:** Systemic vasodilation is a potential adverse effect of local anesthetics, but it is not the most critical concern when administering large doses intravenously.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the dose of local anesthetic is the most critical factor in determining systemic toxicity. The maximum dose of a local anesthetic should be carefully calculated based on the patient's weight, the site of administration, and the type of local anesthetic used.

**Correct Answer: C. Cardiac toxicity**