Is high unemployment one problem that may result when a nation imports more than it exports?

Yes it is an issue. The finace gained from over seas trade is vital as the GDP (Gross domestic Product) requires exports to boost cash flow

GDP = C + G + I + NX

where:

"C" is equal to all private consumption, or consumer spending, in a nation's economy

"G" is the sum of government spending

"I" is the sum of all the country's businesses spending on capital

"NX" is the nation's total net exports, calculated as total exports minus total imports. (NX = Exports - Imports)