It looks like you are using an ANN for function approximation where your target is a continuous variable(?). If so, the uniformity of input data spread over all the dimensions and their range and scale can have a strong impact on how well your ANN works. It has been noticed that, even if there is dense coverage of datapoints over the space of the inputs, an ANN can still have a problem making a good prediction. (I have actually had to smooth the input data $\rightarrow$ i.e., cubic splines, to improve uniformity of datapoint coverage over the range and scale of inputs, before the MSE stabilized and decreased substantially). Therefore, straightforward use of raw input data may not help the situation. If you were performing classification analysis, you would need to use the softmax function on the output side -- but it looks like you are merely performing function approximation. You might also try a linear function (identity) on the output side, and what happens on the output side, because the distribution of your target $y$-variable $[y=f(x_1,x_2,...,x_p)]$ can affect the MSE as well. You could also consider an RBF network, or SOM-ANN, which will reduce dimensionality of your inputs. Lastly, correlation between input features degrades learning speed, since an ANN will waste time learning the correlation between inputs. This is why many use PCA on inputs first, and then input e.g. the 10 PCs associated with the greatest eigenvalues -- effectively decorrelating features so they are orthogonal.
Update(4/27/2016):
A way to more evenly distribute randomly sampled points for inputs to a function approximation problem using an ANN is to employ Latin Hypercube Sampling (LHS) from $\{x,y\}$ in order to predict $\hat{z}$. To begin, split up the range of $x$ and $y$ into $M=10$ uniformly spaced, non-overlapping bins -- the result is a $10\times 10$ square grid with 100 elements (cells) -- call this a ``range grid.'' Next, sample one of the 100 cells, and from this cell draw a random pair of $\{x,y\}$ values from within the range of the bin walls for $x$ and $y$ (of the selected cell), and then block that row and column out from further selection. Next, draw another random element from a row and column that hasn't been sampled from yet, and draw a pair of random $\{x,y\}$ from within that cell. Continue until all rows and column have been selected once. The 10 samples of $\{x,y\}$ will provide pairs of points with no overlap, which is a good way to feed $\{x,y\}$ to an ANN for an $\{x,y,z\}$ problem, or multiple feature problem $\{x_1,z_2,\ldots,x_p\}$.
If you want 100 pairs of $\{x,y\}$, you can start with the combination $\{1,2,3,4,5,6,7,8,9,10\}$. Next, identify 10 permutations for this combination to generate a $10 \times 10$ ``row'' matrix $\mathbf{R}$:
$\{3,2,10,4,1,5,7,9,8,6\}$, $\{2,4,3,1,5,6,10,8,9,7\}$,...,$\{9,1,2,10,5,6,7,8,3,4\}$.
which will give 100 integer values for sampling rows.
Next, generate a $10 \times 10$ ``column'' matrix $\mathbf{C}$ using another set of 10 different permutations:
$\{5,8,10,4,9,3,7,1,2,6\}$, $\{3,7,4,1,5,6,10,8,9,2\}$,...,$\{6,9,2,7,5,1,10,8,3,4\}$
which will provide 100 integers for sampling columns.
The first random draw using the above matrices would be from row 3 and col 5 in the original 10 by 10 grid ``range grid'' of 100 bins for $x$ and $y$. This is another form of LHS.
If you need more than 100 $\{x,y\}$ pairs, then just increase the number of permutations used, and don't be stingy as there are 10! permutations.
Best Answer
I am opposed to cutting values of, since this will lead to an undifferentiable transfer function and your gradient based training algorithm might screw up.
The sigmoid function at the output layer is fine: $\sigma(x) = \frac{1}{1 + e^{-x}}$. It will squash any output to lie within $(0, 1)$. So you can get arbitrarily close to the targets.
However, if you use the squared error you will lose the property of a "matching loss function". When using linear outputs for a squared error, the derivatives of the error reduce to $y - t$ where $y$ is the output and $t$ the corresponding target value. So you have to check your gradients.
I have personally had good results with sigmoids as outputs when I have targets in that range and using sum of squares error anyway.