What are some restrictions when converting Montgomery Curves into Weierstrass Curves? I want to represent a Montgomery Curve (curve25519) in Weierstrass form as a personal exercise.

After doing some math and referencing the conversion equation at http://en.wikipedia.org/wiki/Montgomery_curve, several of my terms contain decimals, which I believe is incorrect. Namely, 

(3-A^2) / (3*B^2) 

is a decimal, when A = 486662 and B = 1 and doing it directly. 

Note that (3-A^2) is negative, so I added the modulus to it to make it positive, which then enables the division by 3 properly as shown here, b

Are there restrictions on which Montgomery curves can be converted to Weierstrass curves?
My comment already gave you the answer; I'm submitting an official answer to give you something to upvote :-)  

An elliptic curve is defined within a field; in the case of curve25519, it is defined within the field $GF(2^{255}-19)$; this is a prime field, because $2^{255}-19$ is prime.

So, when we get to the conversion formulas such as $\frac{3 - A^2}{3\cdot B^2}$, this formula is done within the field the curve is defined in.

Because this is a prime field, addition and multiplication can be implemented by addition and multiplication modulo $2^{255}-19$.  However, division is trickier; it's typically done by computing the modular inverse of the divisor.

As for your question:


  Are there restrictions on which Montgomery curves can be converted to Weierstrass curves?


No, there are no restrictions; all Elliptic curves are isomorphic to some curve in Weierstrass form.  The Wikipedia page you gave gives an explicit mapping from a Montogomery curve into Weierstrauss form.

The one glitch is converting the Curve25519 generator, which is defined as $x=9$; they omit the y-coordinate, and hence corresponds to two elliptic curve points (as there are two different solutions on the curve equation with $x=9$).  This translates into two different points on the Weierstrass curve (which share the $x$ coordinate as well); you can either say that the conversion is that translated $x$ coordinate, or arbitrarily pick one of the valid $y$ coordinates.