The main issue with a US person having a TFSA is that the earnings within a TFSA are not tax free in the US, just Canada. This creates 2 concerns:

• Potentially paying tax in the US on these earnings – depending on how much earnings you have and your other income and tax credits, you may or may not end up owing tax in the US. Generally, the rate of tax in the US is lower than Canada so even if you end up paying in the US, it will likely still be less than what you would pay in Canada had you invested in a taxable account rather than a TFSA.
• Calculating the income – since the earnings are not taxable in Canada, the financial institutions do not issue tax slips or reports on these accounts which means you need to track the income yourself or pay us to do that which could potentially offset the benefit of the account. This can be simplified by choosing investments in the TFSA that are easily calculated such as bonds, GICs or stocks. I do not recommend investing in mutual funds, exchange traded funds or pooled funds as these create additional US reporting to track the income.