I would like pile on with the recommendations for using activeshare.info. However, active share data is only available for mutual funds, so the use cases are limited.
As your question title implies, "detecting" a managers active bets is a function of differentiating them from passive bets.
From Investopedia entry on 13-F "Alpha Cloning":
Portfolio managers can't pick stocks - this is a common saying in
popular press and between proponents of index investments. But
research shows it is not such an evident truth. Mutual/hedge fund
managers in reality can pick stocks but are often too diversified and
their "best picks" therefore cannot deliver such a spectacular
performance as fund's performance is dragged down by rest of the
portfolio. The 13F Fillings Following system is based on assumption
that stocks in which mutual fund managers (and hedge fund managers)
are mostly concentrated (their best ideas) are stocks which will
outperform the broad equity index. SEC 13F fillings could be used to
track top holdings positions in mutual funds.
When an appropriate benchmark is ambiguous (as is often the case for the general case of active management), treating every fund as its own benchmark overcomes the biases you mention in (1) and (2). This benchmark holds every stock in the manager's portfolio and weights each holding "passively". Passive weighting in this context usually means public float adjusted, since this requires also no active management and is what is reflect in most major indices. "Passive" can also be more broadly interpreted to mean any weighting schema which does not involve active bet sizing (e.g., equal weighting).
Treating each portfolio as it own benchmark gets around the issue of identifying active weighting. This method is most robust for funds with diversified holdings ($\ge 30 ???$) However, it is limited due to the fact that skill also involves active selection.