AMOS gives an option for drawing co variances between error terms (in modification indices) to improve the values of model fitness. to what extant, it could be used? and other implications related to this
Generally, as with any other part of a CFA model (or other SEM), measurement errors should only be allowed to covary when there are sound theoretical reasons.
Non-zero error covariance means that the two indicators covary beyond the covariance modeled by the common factor (or the covariance between factors). There may be good reasons to expect this. For example, in longitudinal modeling, error covariance between the same item(s) measured repeatedly over time is often allowed (e.g., Brown, 2015). This is because there may be covariance simply due to the fact that the indicators are the same.
If each indicator is only used once, there are fewer justifications. Reverse-coded items may be one of them, but I would check the literature on that, e.g., Podsakoff, MacKenzie, & Podsakoff (2012).
A common problem is that some researchers allow for error covariances to improve model fit (based on modification indices) without good reasons. This is often inappropriate because it is data-driven (and capitalizes on chance). Even worse, when undisclosed it may be considered cheating. That is why some people (inlcunding myself), when reviewing papers, check whether the reported number of degrees of freedom matches the number that should result from the hypothesized model structure. A discrepancy raises red flags.
For more on this issue, see Landis, Edwards, & Cortina (2009).
Brown, T. A. (2015). Confirmatory factor analysis for applied research. Guilford Publications.
Landis, R. S., Edwards, B. D., & Cortina, J. M. (2009). On the practice of allowing correlated residuals among indicators in structural equation models. In C. E. Lance, R. J. Vandenberg (Eds.), Statistical and methodological myths and urban legends: Doctrine, verity, and fable in the organizational and social sciences, 195-214.
Podsakoff, P. M., MacKenzie, S. B., & Podsakoff, N. P. (2012). Sources of method bias in social science research and recommendations on how to control it. Annual Review of Psychology, 63, 539-569.
Please see the "Handbook of Structural equation modelling" written by Zainudin Awang (2015). Or Search Zainudin Awang in research gate for many papers related with SEM-AMOS
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