The problem is most likely caused by how you calculate your tile positions in combination with float rounding.

For example, mathematically equal multiplications and additions might not equal the exact same value. For example

might not give the exact same result as

The reason why I took this exact example is because that's most likely what you're doing for your sprite positions (or what LibGDX does). Consider a tile, it goes from

to

1
| x2 = tileX * tileSize + tileSize; |

However, the tile next to it at index tileX+1 will start at

1
| x1 = (tileX + 1) * tileSize; |

Now there's a chance for those two to be different since

1 2 3
| tileX * tileSize + tileSize (tileX + 1) * tileSize |

Rounding the values therefore eliminates the problem, but is not a very elegant solution. =S